P--vortices and Drama of Gribov Copies. \vskip-30mm \rightline{ITEP-TH-50/00} \vskip 26mm
V.G.~Bornyakov$^{a,b}$
D.A.~Komarov$^{b}$ and M.I.~Polikarpov$^{b}$
{B.Cheremushkinskaya 25, Moscow, 117259, Russia}
We present results of the careful study of the Gribov copies problem in $SU(2)$ lattice gauge theory for the direct maximal center projection widely used in confinement studies. Applying simulated annealing algorithm we demonstrate that this problem is more severe than it was thought before. The projected (gauge noninvariant) string tension is not in the agreement with the physical string tension. We do not find any indications that P--vortices reproduce the full $SU(2)$ string tension neither in the infinite volume limit nor in the continuum limit.
drama.tex
\documentclass[12pt]{article}
\usepackage{epsfig}
\usepackage{amsfonts}
\usepackage{amssymb}
\setlength{\textheight}{19.5cm}
\setlength{\textwidth}{160mm}
\setlength{\oddsidemargin}{0cm}
\setlength{\evensidemargin}{0cm}
\newcommand{\be}{\begin{equation}}
\newcommand{\en}{\end{equation}}
\newcommand{\eqa}{\begin{eqnarray}}
\newcommand{\ena}{\end{eqnarray}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\ra}{\rightarrow}
\newcommand{\ttbs}{\char'134}
\newcommand{\tr}{\mbox{Tr}}
\newcommand{\noi}{\noindent}
\newcommand{\eq}[1]{(\ref{#1})}

\date{}
\begin{document}
\title{P--vortices and Drama of Gribov Copies.  \vskip-30mm
\rightline{\small ITEP-TH-50/00}
\vskip 26mm
}
\author{V.G.~Bornyakov$^{\rm a,b}$, D.A.~Komarov$^{\rm b}$
and M.I.~Polikarpov$^{\rm b}$\\
\\
$^{\rm a}$ {\small\it Institute for High Energy Physics, Protvino 142284,
Russia}\\
$^{\rm b}$ {\small\it Institute of Theoretical and  Experimental
Physics,}\\
{\small\it B.Cheremushkinskaya 25, Moscow, 117259, Russia}\\ }

\maketitle

\begin{abstract}
We present results of the careful study of the Gribov copies problem in
$SU(2)$ lattice gauge theory for the direct maximal center projection widely
used in confinement studies. Applying simulated annealing algorithm we
demonstrate that this  problem is more severe than it was thought  before.
The projected (gauge noninvariant) string tension is not in the agreement
with the physical string tension. We do not find any indications that
P--vortices reproduce the full $SU(2)$ string tension neither in the
infinite volume limit nor in the continuum limit.  \end{abstract}

\section{Introduction}

The idea that the center vortices are the objects responsible for
confinement in the nonabelian gauge theories is rather old
\cite{center_v,tomb1}.
Recently it has been argued  that the center projection might provide a
powerful tool to investigate this idea \cite{greens1}.
It is suggested that
projection dependent P-vortices defined on the lattice plaquettes are able
to locate thick gauge invariant center vortices and thus provide the
essential evidence for the center vortex picture of confinement. So far 3
different center gauges have been used in practical computations: the
indirect maximal center (IMC) gauge \cite{greens1}, the direct maximal
center (DMC) gauge \cite{greens2} and the Laplacian center gauge \cite{def}
(see also \cite{bvz} for a new proposal).

IMC and DMC gauges suffer from the Gribov copies problem \cite{gribov} and
this technical problem gave rise to several claims and counterclaims. At
present we have a drama in five acts:

{\it i)} Initially there was the claim \cite{greens1, greens2} that the
projected string tension (the string tension which is due to P-vortices)
reproduces the full $SU(2)$ string tension. Thus P-vortices are responsible
for the confinement of color in gluodynamics.

{\it ii)} The problem of Gribov copies has been raised in Ref. \cite{tomb2},
where it has been demonstrated  that there are gauge copies which produce
P-vortices evidently with no center vortex finding ability since projected
Wilson loops have no area law. At the same time these gauge copies
correspond to higher maxima of the gauge fixing functional, than those used
in \cite{greens2}.

{\it iii)} In our previous publications \cite{bkpv1,bkpv2} we confirmed the
existence of two classes of gauge copies:  with nonzero and zero projected
string tension $\sigma_{Z(2)}$. We resolved the problem raised in
\cite{tomb2} since we found the copies with the highest maxima of the gauge
fixing functional which correspond to nonzero $\sigma_{Z(2)}$. At the same
time the value of $\sigma_{Z(2)}$ was essentially lower than that obtained
in \cite{greens2} and in is disagreement with the physical string tension
$\sigma_{SU(2)}$.

{\it iv)} In Refs.~\cite{greens_osaka,bfgo} it has been argued that the
disagreement between $\sigma_{Z(2)}$ and $\sigma_{SU(2)}$ is due to strong
finite volume effects and it disappears on large enough lattices. In
Refs.~\cite{bkpv1,bkpv2,greens_osaka,bfgo} the usual relaxation plus
overrelaxation (RO) algorithm was used to fix the DMC gauge.

{\it v)} Below we present results\footnote{The preliminary results are
presented in Ref.~\cite{bkpv2}}, obtained with the help of more powerful
gauge fixing algorithm, simulated annealing (SA), and show that the problem
of low value of $\sigma_{Z(2)}$ persists even on large lattices with
physical extension up to $3fm$.  We discuss here DMC gauge.  Our results for
IMC gauge will be presented elsewhere.

\section{Gauge fixing procedure}
\subsection{Gribov copies}

Direct maximal center gauge \cite{greens2} in $SU(2)$ lattice gauge theory
is defined by the maximization of
the following functional:

\be F(U) =
\frac{1}{4 V} \sum_{n,\mu} \left( \half\tr U_{n,\mu} \right)^2 = \frac{1}{4
       V} \sum_{n,\mu} \frac{1}{4}\left( \tr_{adj} U_{n,\mu} +1 \right),
     \label{maxfunc}
\en
\noi with respect to local gauge transformations, $U_{n,\mu}$ is the
lattice gauge field, $V$ is the lattice volume. Condition (\ref{maxfunc})
fixes the gauge up to $Z(2)$ gauge transformation, and can be considered
as the Landau gauge for adjoint representation. Any fixed configuration can
be decomposed into $Z(2)$ and coset parts:  $U_{n,\mu} = Z_{n,\mu}
V_{n,\mu}$, where $Z_{n,\mu} = \mbox{sign} \tr U_{n,\mu}$. The plaquettes
$Z_{n,\mu\nu}$ constructed from the links $Z_{n,\mu}$ have values $\pm 1$.
The P-vortices (which  form closed surfaces in 4D space) are made from the
plaquettes, dual to plaquettes with $Z_{n,\mu\nu} = -1$.

Some evidence has been collected, that P-vortices in DMC gauge can serve to
locate gauge invariant center vortices. It has been reported \cite{greens2}
that the expectation value of the projected Wilson loops $W_{Z(2)}$,
computed via linking number of the static quarks trajectories and
P-vortices, have area law. The projected string tension $\sigma_{Z(2)}$ is
very close to the string tension of the nonabelian theory $\sigma_{SU(2)}$.
This fact has been called center dominance. Another important observation
was that the density of P-vortices scales as a physical quantity
\cite{greens2,tubing}.

The main problem of DMC gauge fixing is that the functional $F(U)$
\eq{maxfunc} has many local maxima.  This is the analogue of the Gribov
problem in continuum gauge theories \cite{gribov} and we call configurations
corresponding to these local maxima Gribov copies. For gauge conditions
with Gribov copies the usual expression for gauge dependent quantities
\cite{mandula} does not provide unambiguous definition (see recent
discussion of this subject in \cite{nakajima}).  It was shown  that for some
gauge conditions the gauge dependent quantities depend strongly on the local
maxima picked up \cite{bmmp,bbms}. Thus to remove this ambiguity it is
necessary to find the global maximum or, if this is impossible, to
approach the global maximum as close as possible\footnote{For another
proposal to solve this problem see e.g. \cite{stochastic}.}.

The usual algorithm for the gauge of the type (\ref{maxfunc}) is the
relaxation algorithm which performs maximization iteratively site by site.
The relaxation becomes more effective if one uses the overrelaxation. It is
also known that the SA algorithm is more effective
than RO algorithm. It is very useful when ambiguities induced by Gribov
copies become severe \cite{bbms,kerler}. For this reason we use
this algorithm for DMC gauge.

We follow procedure proposed and checked in \cite{bbms}: for given
configuration we generate $N_{cop}$ gauge equivalent copies applying random
gauge transformations to the initial configuration, after that we fix the
gauge for each gauge copy thus producing $N_{cop}$ Gribov copies for each
configuration. Then we compute a gauge dependent quantity $X$ on the
configuration corresponding to the Gribov copy with the highest local
maximum of \eq{maxfunc}, $F_{max}(N_{cop})$. Averaging over statistically
independent gauge field configurations and varying $N_{cop}$ we obtain the
function $<X(N_{cop})>$ and extrapolate it to $N_{cop} \ra \infty$ limit.
This should provide a good estimation for $<X>$ computed on the global
maximum unless the algorithm in use produces local maximum far from the
global ones.

Note that there exists another proposal \cite{parfac} for the gauge fixing
procedure which is free of gauge copies problem. In some particular limit
this procedure corresponds to the search of the global maximum.  There is
also a class of gauge conditions \cite{vds,def,bvz} which do not suffer from
the gauge copies problem.

\subsection{Simulated annealing algorithm}

The functional $F(U)$ can be considered \cite{saa} as the spin action:

\begin{equation}
S(s)=F(U^g) =
\frac{1}{16 V} \sum_{n,\mu} \tr_{adj}\left( s_n U_{n,\mu} s_{n+ \hat{\mu}}
+1 \right)
\end{equation}
\noindent
where the ``spin variable'' $s_n$, is the gauge transformation matrix in
the adjoint representation:
$s_{n,ab}=\frac{1}{2}tr(\sigma_ag_n\sigma_bg^{\dagger}_n)$ .

The lattice field $U_{n,\mu}$ plays the r\^ole of (almost) random local
couplings. Maximization of the functional $F(U^g)$ is equivalent to
decreasing the auxiliary temperature $T$ of the statistical system with
the partition function,

\begin{equation}
  Z = \sum_{\{s_n\}} \exp\left(\frac{1}{T}S(s)\right)\quad.
\end{equation}

One starts with equilibrating this spin glass at high temperature.
Subsequently the temperature, $T$, is decreased adiabatically. In the limit
$T \ra 0$ the system approaches the ground state, i.e.  the maximal value of
$S(s)$. Our SA implementation consists of the following three steps:

\begin{enumerate}
\item Thermalization at $T=1.16$.
\item Gradual decreasing of $T$ down to $T=0.02$.
\item Final maximization by means of the RO algorithm.
\end{enumerate}


In steps 1 and 2 an updating of the spin configuration was done with
Metropolis algorithm. The temperature was lowered after every sweep by the
quantity $\delta T (T)$. $\delta T (T)$ has been tuned such that the spin
action increased about linearly with the number of iteration sweeps.  This
has been realized by subdividing full range [0.02,1.16] into 38 intervals of
width $\Delta T=0.03$. The corresponding differences of the average action
$\Delta \bar{S}(T)>=\bar{S}(T)-\bar{S}(T-\Delta T)$ have been computed on equilibrated
configurations and were found to be very stable against statistical
fluctuations among different Monte Carlo configurations. We used the same
$\delta T (T)$ for all volumes at given value of gauge coupling $\beta$ and
slightly modified it for different $\beta's$. The number of sweeps to be
performed within each interval $(T-\Delta T,T]$ was chosen to be
proportional to $\Delta \bar{S}(T)$ and, subsequently, the corresponding value of
$\delta T(T)$ has been determined. To approach close enough to
the equilibrium we have to perform about 2000 sweeps at the step 2 (for step
1 only 20 sweeps was enough). Finally, at step 3 it is necessary to make
$O(100)$ sweeps of the RO algorithm to satisfy convergence criterion. In
total this procedure was essentially more costly than the RO algorithm, also
it gives the higher maximum of the functional (\ref{maxfunc}).

\section{Results}

\subsection{Details of simulation}
Our computations have been performed on lattices
$12^4, 16^4,
20^4$ and $24^4$ for $\beta=2.4$ and $16^4,20^4$ for $\beta=2.5$.
The number of configurations was $150$ for $12^4,$ $50$ for $16^4,$
$30$ for $20^4$, $20$  for $24^4$.

Using the described above gauge fixing procedure we calculate various
observables as functions of the number of randomly generated gauge copies
$N_{cop}$. To make computations feasible we reduce the maximal
value of $N_{cop}$ on large lattices, see Table 1.

\begin{table}[h]
\caption{The maximal values of $N_{cop}$ for various lattices.} \label{t1}
\setlength{\tabcolsep}{0.55pc}
\begin{center}
\begin{tabular}{c|cccc}  \hline
&$L=12$ & $L=16$ & $L=20$& $L=24$  \\ \hline
$\beta=2.4$ &10 &7&7&4  \\
$\beta=2.5$ &--&7&7&7  \\ \hline
\end{tabular}
\end{center}
\end{table}


The projected Wilson loops $W_{Z(2)}(C)$ are defined as

\[ W_{Z(2)}(C)=<\exp\{i\pi {\cal L}(\Sigma_P,C)\}> \]
where  ${\cal L}(\Sigma_P,C)$ is the 4D linking number of the closed
surface, $\Sigma_P$, formed by P-vortex and closed loop $C$.
We used two ways to estimate projected string tension $\sigma_{Z(2)}$:
from the Creutz ratios

\be\label{CRZ2}
\chi_{Z(2)} (I,I)  =
-\log\frac{W_{Z(2)}(I,I)W_{Z(2)}(I+1,I+1)}{W_{Z(2)}(I,I+1)W_{Z(2)}(I+1,I)}
\, ;
\en
and fitting static potential
\[ V_{Z(2)}(R) = -\lim_{T\rightarrow\infty} \log\frac{W_{Z(2)}(R,T+1)}{W_{Z(2)}(R,T)} \]
to the usual form
\begin{equation}
V_0+c/R+\sigma_{Z(2)}a^2R \, .
\label{potfit}
\end{equation}

The P-vortex density $\rho$ is another quantity of interest.
It is defined as follows
\[ \rho = \frac{1}{12 \cdot V } \sum_{n;\mu > \nu} (1-Z_{n,\mu\nu}). \]

\subsection{Maximized functional and extrapolation to $N_{cop} \to \infty$}

In DMC gauge the average value $<F_{max}>$ is an important indicator of the
quality of the gauge fixing since gauge noninvariant observables we are
measuring are strongly correlated with $<F_{max}>$. In Fig.1 we plot
$<F_{max}>$ as a function of $N_{cop}$. For comparison we show the results
for RO algorithm and the algorithm suggested in \cite{tomb2} : before
applying RO algorithm the random gauge copy was fixed to Landau gauge. We
call it LRO algorithm. One can see that SA algorithm indeed produces highest
maxima. We checked that this is true for other lattices as well.

\hspace*{2cm} \input{fig1.tex}
\begin{figure}[tbh]
\begin{centering}
\caption{The average value of the highest local maxima $<F_{max}>$
for 3 algorithms as a function of $N_{cop}$; $L=16,\beta=2.5$. The solid
lines are the fits using the asymptotic expression (\ref{fit1}).
}
\end{centering}
\end{figure}

One can draw two conclusions from Fig.1.  First, it is clear that the local
maxima generated with LRO procedure of \cite{tomb2} can be safely ignored.
Second, RO algorithm does not permit to reach the global maxima and results
obtained with this algorithm must be revised with the help of SA algorithm.
As we mentioned the gauge dependent quantities are strongly correlated with
the value of $F_{max}$.

The important question is how close we approach
the global maximum. Theoretically SA algorithm permits to find the global
maximum.  In practice this is complicated task because of large
autocorrelation length at small temperature $T$. We checked for a few
configurations that increasing the number of sweeps in our SA algorithm by
factor 5 does not lead to any essential change in $F_{max}$. This indicates
that we are close to the equilibrium during SA cooling and thus our results
are close to the global maximum when we make the extrapolation to $N_{cop}
\to \infty$ limit.

As we show in the Appendix there are 2 possibilities
for dependence of $<F_{max}>$ on $N_{cop}$.
Our data show that
at small $N_{cop}$ eq.(\ref{fit2}) provides better fit while at large
$N_{cop}$ eq.(\ref{fit1}) is better. For this reason we use eq.(\ref{fit1})
to extrapolate the data to $N_{cop} \to \infty$ limit. In Fig.2 we depict
$\chi_{Z(2)}(5,5)$ and $<\rho>$ as
functions of $<F_{max}>$. The linear dependence seen in this figure
proves that the use of the same
fitting function (eq.  (\ref{fit1}))  for $<F_{max}>$ and for
$\chi_{Z(2)}(I,I)$ and  $<\rho>$ is indeed well grounded.

\vspace*{0.5cm}
\hspace{2cm}\input{fig2.tex}
\begin{figure}[tbh]
\begin{centering}
\caption{ $\chi_{Z(2)}(5,5)$ and $<\rho>$ vs. $<F_{max}>$
for $L=20,\beta=2.4$.
}
\end{centering}
\end{figure}

\subsection{P-vortex density}

The physical density of P-vortices $<\rho/a^2>$ is the important indicator
of their relevance for the infrared physics. If, e.g., it goes to zero
in the continuum limit, then P-vortices cannot play any important
role. It is known
that for the completely uncorrelated vortices
$<\rho/a^2>=\frac{1}{2}\sigma_{Z(2)}$ \cite{tubing}.

To compare the scaling of density with that of the unprojected string
tension we show in Fig.3 the ratio\footnote{$\sigma_{SU(2)}a^2 =0.0728(6)$
for $\beta=2.4 \cite{phm},~0.0350(4)$ for $\beta=2.5$ \cite{bss}}
$<\rho>/\sigma_{SU(2)}a^2$.
One can see that for two $\beta$ values this ratio is almost the
same, i.e. scaling properties of $<\rho/a^2> $ and $\sigma_{SU(2)}$
are similar. The volume dependence is rather weak.
Our value for $<\rho>$ is essentially lower than that obtained in
\cite{bfgo} and this difference increases with $\beta$.  It will be clear
from our results in the next section that $<\rho/a^2> \approx
\sigma_{Z(2)}$, i.e.  P-vortices are far from being uncorrelated. On the
other hand (at least on the lattices up to $24^4$) the density of P-vortices
does not reproduce the full string tension, $\sigma_{SU(2)}$, as it was
suggested in Ref.~\cite{greens2}.

\hspace{2cm}\input{fig3.tex}
\begin{figure}[tbh]
\begin{centering}
\caption{The ratio $<\rho>/\sigma_{SU(2)}a^2$ vs. $N_{cop}$.
The solid lines are the fits obtained using asymptotic expression
(\ref{fit1}). } \end{centering}
\end{figure}

\subsection{Projected string tension $\sigma_{Z(2)}$}
\subsubsection{Creutz ratio $\chi_{Z(2)}$}

At first we discuss the final volume effects. In Fig.4 we show the
dependence of $\chi_{Z(2)}(4,4)$ on $N_{cop}$ for $\beta=2.4$. From the
figure one can see that finite volume effects are essential for $L=12$ only.
For the other values of $I$ we obtained the similar behavior. At $\beta=2.5$
we found a sizable finite volume effects only on $L=16$ lattice.

\hspace{2cm}\input{fig4.tex}
\begin{figure}[tbh]
\begin{centering}
\vspace*{-0.5cm}
\caption{The dependence of the Creutz ratios $\chi_{Z(2)}(4,4)$
on the number of gauge
copies $N_{cop}$ for $\beta=2.4$. The solid lines are fits using eq.
(\ref{fit1}).
}
\end{centering}
\end{figure}

Usually one uses the Creutz ratio $\chi_{Z(2)}(I,I)$ (\ref{CRZ2}) to
estimate the projected string tension because the dependence on $I$ was
found to be rather weak. In our study we found that it was not quite true.
In Fig.5 we plot the ratio $\chi_{Z(2)}(I,I)/\sigma_{SU(2)}a^2$
as a function of the dimensional distance~\footnote{The physical distance
scale is set by the value $\sigma_{SU(2)}=(440~Mev)^2$}  $r=I\cdot a$. The
data shown were obtained for maximal values of $N_{cop}$ given in Table 1. The values
extrapolated to $N_{cop}\to\infty$ limit are only slightly lower.
One can see that $\chi_{Z(2)}(I,I)$ is not constant but increases with $I$
at least in the range $0.3fm \lesssim I\cdot a \lesssim 0.7fm$. The similar behavior can be
seen in Fig.3 of \cite{bfgo}. We found that this effect weakens, when
$N_{cop}$ increases, but does not disappear completely. It is evident from
this figure that even on our largest lattice ($L=24$ at $\beta=2.4$), which
has extension in physical units of about $3fm$, $\chi_{Z(2)}(I,I)$ is much
lower than the unprojected string tension. This invalidates the suggestion
of \cite{bfgo} that $\chi_{Z(2)}(I,I)$ approaches $\sigma_{SU(2)}a^2$ on
lattices larger than the size of $Z(2)$-vortex ($\sim 1fm$). Let us remind
that the authors of Ref.~\cite{bfgo} have used the RO algorithm to fix the
gauge, while we are using the SA algorithm.

\begin{center}
\hspace{2cm}\input{fig5.tex}
\begin{figure}[tbh]
\vspace*{-0.5cm}
\caption{The dependence of $\chi_{Z(2)}(I,I)/\sigma_{SU(2)} a^2$ on the
distance in physical units. $N_{cop}$ are the largest values used for the
given lattice (see Table 1).} \end{figure} \end{center}


Our estimation for $\sigma_{Z(2)}/\sigma_{SU(2)}$ made from projected Creutz
ratio measured at distances $0.7-0.9 fm$ is 0.66(2).
Comparing our data
obtained at given $\beta$ on lattices of various size (see Fig.5), we can
conclude that for lattices of physical extension larger than $1.7 fm$ there
are no sizable finite volume effects for the string tension extracted from
the Wilson loops of the size $\lesssim 1fm$. Still we cannot exclude that
the projected string tension, measured from projected Wilson loops with a
very large extension, approaches the full string tension.

\subsubsection{Static potential $V_{Z(2)}(R,T)$}

In view of the dependence of $\chi_{Z(2)}(I,I)$ on $I$ it is interesting to
study the projected static potential
$V_{Z(2)}(R)=\lim_{T \to \infty}V_{Z(2)}(R,T),~~
V_{Z(2)}(R,T)=-\log\frac{W_{Z(2)}(R,T+1)}{W_{Z(2)}(R,T)}$.
As it is seen from Fig.6 $V_{Z(2)}(R,T)$ rises
as a function of $T$.
If we assume that for $W_{Z(2)}(R,T)$ the usual expansion

\be W_{Z(2)}(R,T)= C_0(R)exp\left( -V_{Z(2)}(R)T \right)~ +~
C_1(R)exp\left( -V_1(R)T \right) ~+...
\en
is valid, then such behavior implies that  $C_1(R)<0$.

To compute $V_{Z(2)}(R)$ we first extrapolated $V_{Z(2)}(R,T)$ as a function
of $N_{cop}$ to $N_{cop}~\rightarrow~\infty$ limit and then evaluated $V_{Z(2)}(R)$
using large $T$ values. The results are depicted in Fig.7.

\hspace{2cm}\input{fig6.tex}
\begin{figure}[tbh]
\begin{centering}
\caption{ $V_{Z(2)}(R,T)$ as a function of $T$ for several values of $R$.~
$L=24,~ \beta=2.4$,~ $N_{cop}=4$ .
}
\end{centering}
\end{figure}

\hspace{2cm}\input{fig7.tex}
\begin{figure}[tbh]
\begin{centering}
\caption{The static potential $V_{Z(2)}(R)$.~
$L=24,~ \beta=2.4$.~The solid line is fit using eq.(\ref{potfit}).
}
\end{centering}
\end{figure}
\newpage

The value of $\sigma_{Z(2)}$ obtained from the projected static potential is
in agreement with that obtained from the projected Creutz ratio (Section
3.4.1).


\section{Conclusions}

We made the most careful up to date gauge fixing of DMC gauge employing SA
algorithm. We have shown that this algorithm permits to get the higher local
maximum of the functional $F(U)$ than that obtained before with other
algorithms. Though increment in $<F_{max}>$ looks not impressive it gives
rise to substantial change in the values of gauge noninvariant observables.
This, in turn, brought us to conclusions different from those made in
\cite{bfgo}. We computed the projected string tension $\sigma_{Z(2)}$ and
P-vortex density $<\rho>$ on volumes with physical extension from $1.4fm$ up
to $3fm$.  Our results imply that only on our smallest lattices ($L=12$ for
$\beta=2.4$ and $L=16$ for $\beta=2.5$) there are moderate finite volume
effects. Our data for lattice size larger than $1.7fm$ show the absence of
the finite volume effects.

The ratio of P-vortex density to $\sigma_{SU(2)}$ weakly depends on $\beta$
(see Fig.3) and the early asymptotic scaling of this density (observed in
\cite{greens2,bfgo}) does not exist.

The projected string tension, $\sigma_{Z(2)}$, does not reproduce the full
string tension, $\sigma_{SU(2)}$. The obtained value of the ratio
$\sigma_{Z(2)}/\sigma_{SU(2)} \approx 0.66(2)$ is rather low.
Comparing results
for two lattice spacings we do not see any convergence of this ratio to 1 in
the continuum limit (further studies at larger values of $\beta$ on
larger lattices are important).
Let us remind that abelian monopoles are responsible for
$92\% - 94\%$ of the full $SU(2)$ string tension \cite{bbms,gubali}.

Since the P-vortices in DMC gauge do not reproduce the full $SU(2)$ string
tension they cannot be responsible for confinement. On the other hand the fact
that $\sigma_{Z(2)}$ is of the same order as $\sigma_{SU(2)}$ probably means
that the DMC gauge is close to some ``ideal gauge'' which detect perfectly
\cite{greens1} the thick gauge independent center vortices \cite{jg_priv}.
Recent results \cite{defp} show that an example of such gauge
is the Laplacian Center Gauge which is free of Gribov
copies problem and $\sigma_{Z(2)} \approx \sigma_{SU(2)}$ in this gauge.

\section*{Acknowledgements}

We are grateful to V. Anikeeva and A. Veselov for the help at some stages of
this work. We thank T. Kovacs for the helpful remark. 
This work was partially supported by grants RFBR 99-01230a,
INTAS 96-370, Monbushu grant and CRDF award RP1-2103.

\section*{Appendix A}
\setcounter{equation}{0}
\def\theequation{A.\arabic{equation}}


Let the probability distribution of the random variable $x$ is $p(x)$
and let $p(x)$ is nonzero on the interval $[x_0-\delta_1,x_0+\delta_2]$.
Let us introduce

\[ P(x) = \int_{x_0-\delta_1}^x dy~p(y) \]

\noindent with properties
\[ P^{\prime}(x)=p(x),~~P(x_0-\delta_1) = 0,~~P(x_0+\delta_2) = 1. \]

\noindent
Then probability distribution $P^{(N)}(x)$ to get value x as
maximal out of N attempts  is equal to

\[ P^{(1)}(x) = p(x) \]
\[ P^{(N)}(x) = C_N P(x)^{N-1} p(x)  \]

\noindent
where normalization constant

\[ C_N^{-1} = \int_{x_0-\delta_1}^{x_0+\delta_2}dx~ P(x)^{N-1} p(x)=
\int_{P(x_0-\delta_1)}^{P(x_0+\delta_2)}dP~P^{N-1} = \frac{1}{N} P^N
|^1_0 = \frac{1}{N} \]

\noindent
We have to evaluate

\[ \bar{x}^{(N)} = \int_{x_0-\delta_1}^{x_0+\delta_2}dx~xP^{(N)}(x) =
N\int_{x_0-\delta_1}^{x_0+\delta_2}dx~xp(x)P^{N-1}(x) \]

\[ = x_0 + N\int_{-\delta_1}^{\delta_2}dy~yp(y)P^{N-1}(y)~~ (x=y+x_0) \]

\[ = x_0 + \int_{-\delta_1}^{\delta_2}dy~y \frac{dP^{N}(y)}{dy}
= x_0 + y P^N(y) |_{-\delta_1}^{\delta_2}
- \int_{-\delta_1}^{\delta_2}dy~ P^N(y) \]

\[ = x_0 + \delta_2 - \int_{-\delta_1}^{\delta_2}dy~ P^N(y)
= \bar{x} - \int_{-\delta_1}^{\delta_2}dy~ P^N(y) \]

\noindent
where $\bar{x}=x_0+\delta_2$ is evidently the value of $\bar{x}^{(N)}$
in the limit $N \rightarrow \infty$.
The integral in the last equation can be evaluated for large $N$
in the following way:

\[ I=-\int_{-\delta_1}^{\delta_2}dy~ P^N(y) =
-\int_{-\delta_1}^{\delta_2}dy~ e^{Nlog(P(y))} \]

\noindent
We expand the function $f(y)=log(P(y))$ at its maximum
$y=\delta_2$:

\[ f(y)= \frac{P^{\prime}(\delta_2)}{P(\delta_2)}
\epsilon +
\frac{1}{2}[\frac{P^{\prime\prime}(\delta_2)}{P(\delta_2)}
-(\frac{P^{\prime}(\delta_2)}{P(\delta_2)})^{2}]
\epsilon^2 + ...
 = p(\delta_2)\epsilon +
\frac{1}{2}[p^{\prime}(\delta_2) - p^2(\delta_2)] \epsilon^2
+... ,~~~~\epsilon=y-\delta_2  \]


\noindent
Then
\[ I = -\int_{-\delta_1-\delta_2}^{0}d\epsilon~
e^{N \left( p(\delta_2)\epsilon +
\frac{1}{2}[p^{\prime}(\delta_2) - p^2(\delta_2)] \epsilon^2
 +... \right) } \]

\noindent
 Let us consider 2 cases:
\begin{itemize}
\item [1.]
$p(\delta_2) \ne 0$.

\[I= -\frac{1}{N}\int_{-N(\delta_1+\delta_2)}^{0}d\epsilon~
e^{p(\delta_2)\epsilon
+ \frac{1}{2N}[p^{\prime}(\delta_2) - p^2(\delta_2)] \epsilon^2
+... }
=-\frac{1}{Np(\delta_2)}\left( 1+O \left( \frac{1}{N} \right) \right) \]

Thus in this case the fitting function for numerical data  should be:

\begin{equation}
f_1(N)=\bar{x}+\frac{C_1}{N}+\frac{C_2}{N^2}+...
\label{fit1}
\end{equation}

\item [2.]
$p(\delta_2) = 0$.

\[I= -\frac{1}{\sqrt{N}}\int_{-\sqrt{N}(\delta_1+\delta_2)}^{0}d\epsilon~
e^{ \frac{1}{2}[p^{\prime}(\delta_2) - p^2(\delta_2)] \epsilon^2
+... }
 \]

Then fitting function is
\begin{equation}
f_2(N)=\bar{x}+\frac{C_1}{\sqrt{N}}+\frac{C_2}{N}+...
\label{fit2}
\end{equation}

\end{itemize}
If $p(\delta_2)$ is a very small number then there might exist
interval of $N$ where eq. (\ref{fit2})
provides better fit, while in the limit of large $N$ eq.(\ref{fit1})
is valid.
The data for our observables ($<F_{max}>$, $<\rho>$, 
$\chi_{Z(2)}(I,I)$)
indicates just this situation. For this reason we made fits with
eq.(\ref{fit1}) discarding small values of $N_{cop}$.

\begin{thebibliography}{99}
\newcommand{\npb}[1]{{\it Nucl.~Phys.}~{\bf B#1}\ }
\newcommand{\plb}[1]{{\it Phys.~Lett.}~{\bf #1B}\ }

\bibitem{center_v} G. 't Hooft, \npb{138},1 (1978);\\
J.M. Cornwall, \npb{157},392 (1979); \\
G. Mack, in Recent Developments in Gauge Theories, ed. by G. 't Hooft et al.
(Plenum, New York, 1980); \\
H.B. Nielsen and P. Olesen, \npb{160} (1979) 380; \\
J. Ambjorn and P. Olesen, \npb{170} (1980) 60; 265.

\bibitem{tomb1}  T.G. Kovacs and E. T. Tomboulis,
{\it J.Math.Phys.} {\bf 40} (1999) 4677.

\bibitem{greens1} L. Del Debbio, M. Faber, J. Greensite and S. Olejnik,
{\it Phys.Rev.} {\bf D55} (1997) 2298.

\bibitem{greens2} L. Del Debbio, M. Faber, J. Giedt, J. Greensite and S.
Olejnik, {\it Phys.Rev.} {\bf D58} (1998) 094501.

\bibitem{def}
Ph. de Forcrand and M. D'Elia, {\it Phys.Rev.Lett.} {\bf 82} (1999) 4582; \\
C. Alexandrou, M. D'Elia and Ph. de Forcrand,~ {\it Nucl.Phys.} {\bf B}
[Proc.Suppl.] {\bf 83}(2000)~437.

\bibitem{bvz} B.L.~Bakker, A.I.~Veselov and M.A.~Zubkov,
hep-lat/007022.

\bibitem{gribov} V.N.~Gribov, \npb{139} (1978) 1.

\bibitem{tomb2}  T.G. Kovacs and E.T. Tomboulis,
{\it Phys.Lett.} {\bf B463} (1999) 104.

\bibitem{bkpv1} V.G. Bornyakov, D.A. Komarov, M.I. Polikarpov
and A.I. Veselov, {\it JETP Lett.} {\bf 71} (2000) 231.

\bibitem{bkpv2} V.G. Bornyakov, D.A. Komarov, M.I. Polikarpov
and A.I. Veselov, To be published in Proceedings of the
International Symposium on Quantum Chromodynamics and Color
Confinement (Confinement 2000), Osaka, Japan, 7-10 Mar 2000.

\bibitem{greens_osaka} J. Greensite, hep-lat/0005001.

\bibitem{bfgo} R. Bertle, M. Faber, J. Greensite, S. Olejnik,
 hep-lat/0007043.

\bibitem{tubing} K. Langfeld, O. Tennert, M. Engelhardt and H. Reinhardt,
{\it Phys.Lett.} {\bf B452} (1999) 301.

\bibitem{mandula} J.E.~ Mandula and M.C.~ Ogilvie, \plb{185} (1987)~127.

\bibitem{nakajima} H.~Nakajima, S.~Furui and A.~Yamaguchi,~
hep-lat/0007001.

\bibitem{bmmp} A.~Nakamura and M.~Plewnia, \plb{255} (1991)~274; \\
V.~Bornyakov, V.K.~Mitrjushkin, M.~M\"uller-Preussker
 and F.~Pahl, \plb{B317} (1993)~596.

\bibitem{bbms} G.S. Bali, V. Bornyakov, M. M\"uller-Preussker and K.
Schilling, {\it Phys.Rev.} {\bf D54} (1996) 2863.

\bibitem{stochastic} F. Shoji, T. Suzuki, H. Kodama and A. Nakamura,
\plb{476} (2000) 199.

\bibitem{kerler} G. Damm, W. Kerler, \plb{397} (1997) 216.

\bibitem{parfac} S.~Fachin and C.~Parrinello,
{\it Nucl. Phys.} {\bf B} [Proc.~Suppl.] {\bf 26}(1992)~429.

\bibitem{vds} J.C. Vink, U.-J. Wiese,
{\it Phys.Lett.} {\bf B289} (1992) 122; \\
A.J. van der Sijs, {\it Prog.Theor.Phys.Suppl.} {\bf 131} (1998) 149.

\bibitem{saa} S.~Kirkpatrick, C.D.~Gelatt Jr., M.P.~Vecchi,
{\it Science} {\bf 220} (1983) 671; V.~Cerny,
{\it J.\ Opt.\ The.\ Appl.\ } {\bf 45}
(1985) 41.

\bibitem{phm} S. Perantonis, A. Huntley and C. Michael,
\npb{326} (1989) 544.

\bibitem{bss} G.S. Bali, K. Schilling and C. Schlichter,
{\it Phys.Rev.} {\bf D51} (1995) 5165.

\bibitem{gubali} F.V. Gubarev, E.M. Ilgenfritz, M.I. Polikarpov and
T.~Suzuki, {\it Phys. Lett.} {\bf B468} (1999) 134.

\bibitem{jg_priv} J. Greensite, private communication.

\bibitem{defp} Ph. de Forcrand and M. Pepe, hep-lat/0008016.

\end{thebibliography}


\end{document}








fig1.tex
% GNUPLOT: LaTeX picture with Postscript
\begingroup%
  \makeatletter%
  \newcommand{\GNUPLOTspecial}{%
    \@sanitize\catcode`\%=14\relax\special}%
  \setlength{\unitlength}{0.1bp}%
{\GNUPLOTspecial{!
%!PS-Adobe-2.0 EPSF-2.0
%%Title: fmax_all_tex.tex
%%Creator: gnuplot 3.7 patchlevel 1
%%CreationDate: Thu Aug 17 21:29:54 2000
%%DocumentFonts: 
%%BoundingBox: 0 0 288 216
%%Orientation: Landscape
%%EndComments
/gnudict 256 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/userlinewidth gnulinewidth def
/vshift -33 def
/dl {10 mul} def
/hpt_ 31.5 def
/vpt_ 31.5 def
/hpt hpt_ def
/vpt vpt_ def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def
  /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke userlinewidth 2 mul setlinewidth } def
/AL { stroke userlinewidth 2 div setlinewidth } def
/UL { dup gnulinewidth mul /userlinewidth exch def
      10 mul /udl exch def } def
/PL { stroke userlinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 1 0 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 1 0 DL } def
/LT2 { PL [2 dl 3 dl] 0 0 1 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/Pnt { stroke [] 0 setdash
   gsave 1 setlinecap M 0 0 V stroke grestore } def
/Dia { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  Pnt } def
/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  Pnt } def
/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  Pnt  } def
/Star { 2 copy Pls Crs } def
/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V  hpt2 0 V  0 vpt2 V
  hpt2 neg 0 V  closepath fill } def
/TriUF { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath fill } def
/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke
  Pnt  } def
/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath fill} def
/DiaF { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath fill } def
/Pent { stroke [] 0 setdash 2 copy gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore Pnt } def
/PentF { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath fill grestore } def
/Circle { stroke [] 0 setdash 2 copy
  hpt 0 360 arc stroke Pnt } def
/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def
/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450  arc } bind def
/C1 { BL [] 0 setdash 2 copy        moveto
       2 copy  vpt 0 90 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C2 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C3 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C4 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C5 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 90 arc
       2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc } bind def
/C6 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 90 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C7 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 0 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C8 { BL [] 0 setdash 2 copy moveto
      2 copy vpt 270 360 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C9 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 270 450 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill
       2 copy moveto
       2 copy vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C11 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
       2 copy moveto
       2 copy  vpt 270 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C12 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C13 { BL [] 0 setdash  2 copy moveto
       2 copy  vpt 0 90 arc closepath fill
       2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C14 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 360 arc closepath fill
               vpt 0 360 arc } bind def
/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/Rec   { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
       neg 0 rlineto closepath } bind def
/Square { dup Rec } bind def
/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def
/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def
/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def
/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def
/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill
       exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill
       2 copy vpt Square fill
       Bsquare } bind def
/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def
/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill
       Bsquare } bind def
/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill
       Bsquare } bind def
/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def
/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy vpt Square fill Bsquare } bind def
/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def
/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def
/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def
/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def
/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def
/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def
/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def
/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def
/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def
/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def
/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def
/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def
/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def
/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def
/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def
/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def
/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def
/DiaE { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke } def
/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke } def
/TriUE { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke } def
/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke } def
/PentE { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore } def
/CircE { stroke [] 0 setdash 
  hpt 0 360 arc stroke } def
/Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def
/DiaW { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V Opaque stroke } def
/BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V Opaque stroke } def
/TriUW { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V Opaque stroke } def
/TriDW { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V Opaque stroke } def
/PentW { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  Opaque stroke grestore } def
/CircW { stroke [] 0 setdash 
  hpt 0 360 arc Opaque stroke } def
/BoxFill { gsave Rec 1 setgray fill grestore } def
end
%%EndProlog
}}%
\begin{picture}(2880,2160)(0,0)%
{\GNUPLOTspecial{"
gnudict begin
gsave
0 0 translate
0.100 0.100 scale
0 setgray
newpath
1.000 UL
LTb
500 300 M
63 0 V
2167 0 R
-63 0 V
500 691 M
63 0 V
2167 0 R
-63 0 V
500 1082 M
63 0 V
2167 0 R
-63 0 V
500 1473 M
63 0 V
2167 0 R
-63 0 V
500 1864 M
63 0 V
2167 0 R
-63 0 V
500 300 M
0 63 V
0 1697 R
0 -63 V
905 300 M
0 63 V
0 1697 R
0 -63 V
1311 300 M
0 63 V
0 1697 R
0 -63 V
1716 300 M
0 63 V
0 1697 R
0 -63 V
2122 300 M
0 63 V
0 1697 R
0 -63 V
2527 300 M
0 63 V
0 1697 R
0 -63 V
1.000 UL
LTa
500 300 M
0 1760 V
1.000 UL
LTb
500 300 M
2230 0 V
0 1760 V
-2230 0 V
500 300 L
1.000 UP
1.000 UL
LT0
2367 1947 M
263 0 V
-263 31 R
0 -62 V
263 62 R
0 -62 V
2527 1472 M
0 54 V
-31 -54 R
62 0 V
-62 54 R
62 0 V
-1044 6 R
0 56 V
-31 -56 R
62 0 V
-62 56 R
62 0 V
-369 -29 R
0 57 V
-31 -57 R
62 0 V
-62 57 R
62 0 V
-200 -40 R
0 57 V
-31 -57 R
62 0 V
-62 57 R
62 0 V
905 1588 M
0 57 V
-31 -57 R
62 0 V
-62 57 R
62 0 V
-98 -48 R
0 57 V
-31 -57 R
62 0 V
-62 57 R
62 0 V
-79 -49 R
0 57 V
-31 -57 R
62 0 V
-62 57 R
62 0 V
2527 1499 Circle
1514 1560 Circle
1176 1587 Circle
1007 1605 Circle
905 1617 Circle
838 1626 Circle
790 1633 Circle
2498 1947 Circle
1.000 UP
1.000 UL
LT0
2367 1847 M
263 0 V
-263 31 R
0 -62 V
263 62 R
0 -62 V
2527 1288 M
0 70 V
-31 -70 R
62 0 V
-62 70 R
62 0 V
1514 1302 M
0 69 V
-31 -69 R
62 0 V
-62 69 R
62 0 V
-369 -63 R
0 68 V
-31 -68 R
62 0 V
-62 68 R
62 0 V
-200 -64 R
0 67 V
-31 -67 R
62 0 V
-62 67 R
62 0 V
905 1314 M
0 67 V
-31 -67 R
62 0 V
-62 67 R
62 0 V
-98 -65 R
0 67 V
-31 -67 R
62 0 V
-62 67 R
62 0 V
-79 -66 R
0 67 V
-31 -67 R
62 0 V
-62 67 R
62 0 V
-68 -66 R
0 67 V
-31 -67 R
62 0 V
-62 67 R
62 0 V
-59 -66 R
0 67 V
-31 -67 R
62 0 V
-62 67 R
62 0 V
-53 -66 R
0 66 V
-31 -66 R
62 0 V
-62 66 R
62 0 V
-50 -65 R
0 66 V
-31 -66 R
62 0 V
-62 66 R
62 0 V
-46 -66 R
0 67 V
-31 -67 R
62 0 V
-62 67 R
62 0 V
-44 -66 R
0 66 V
-31 -66 R
62 0 V
-62 66 R
62 0 V
-42 -65 R
0 66 V
-31 -66 R
62 0 V
-62 66 R
62 0 V
-41 -66 R
0 66 V
-31 -66 R
62 0 V
-62 66 R
62 0 V
-39 -65 R
0 66 V
-31 -66 R
62 0 V
-62 66 R
62 0 V
-39 -66 R
0 66 V
-31 -66 R
62 0 V
-62 66 R
62 0 V
-37 -65 R
0 65 V
-31 -65 R
62 0 V
-62 65 R
62 0 V
-37 -65 R
0 66 V
-31 -66 R
62 0 V
-62 66 R
62 0 V
-37 -66 R
0 66 V
-31 -66 R
62 0 V
-62 66 R
62 0 V
2527 1323 CircleF
1514 1337 CircleF
1176 1342 CircleF
1007 1345 CircleF
905 1347 CircleF
838 1349 CircleF
790 1350 CircleF
753 1351 CircleF
725 1352 CircleF
703 1353 CircleF
684 1354 CircleF
669 1355 CircleF
656 1355 CircleF
645 1356 CircleF
635 1356 CircleF
627 1357 CircleF
619 1357 CircleF
613 1357 CircleF
607 1358 CircleF
601 1358 CircleF
2498 1847 CircleF
1.000 UP
1.000 UL
LT0
2367 1747 M
263 0 V
-263 31 R
0 -62 V
263 62 R
0 -62 V
2527 480 M
0 56 V
-31 -56 R
62 0 V
-62 56 R
62 0 V
1514 619 M
0 59 V
-31 -59 R
62 0 V
-62 59 R
62 0 V
-369 10 R
0 60 V
-31 -60 R
62 0 V
-62 60 R
62 0 V
1007 732 M
0 61 V
976 732 M
62 0 V
-62 61 R
62 0 V
905 764 M
0 62 V
874 764 M
62 0 V
-62 62 R
62 0 V
838 788 M
0 63 V
807 788 M
62 0 V
-62 63 R
62 0 V
790 808 M
0 64 V
759 808 M
62 0 V
-62 64 R
62 0 V
753 824 M
0 65 V
722 824 M
62 0 V
-62 65 R
62 0 V
725 838 M
0 65 V
694 838 M
62 0 V
-62 65 R
62 0 V
703 850 M
0 65 V
672 850 M
62 0 V
-62 65 R
62 0 V
684 861 M
0 65 V
653 861 M
62 0 V
-62 65 R
62 0 V
669 870 M
0 66 V
638 870 M
62 0 V
-62 66 R
62 0 V
656 878 M
0 66 V
625 878 M
62 0 V
-62 66 R
62 0 V
645 886 M
0 66 V
614 886 M
62 0 V
-62 66 R
62 0 V
635 893 M
0 66 V
604 893 M
62 0 V
-62 66 R
62 0 V
627 899 M
0 67 V
596 899 M
62 0 V
-62 67 R
62 0 V
619 904 M
0 68 V
588 904 M
62 0 V
-62 68 R
62 0 V
613 910 M
0 67 V
582 910 M
62 0 V
-62 67 R
62 0 V
607 914 M
0 68 V
576 914 M
62 0 V
-62 68 R
62 0 V
601 919 M
0 67 V
570 919 M
62 0 V
-62 67 R
62 0 V
2527 508 TriU
1514 648 TriU
1176 718 TriU
1007 763 TriU
905 795 TriU
838 820 TriU
790 840 TriU
753 856 TriU
725 871 TriU
703 883 TriU
684 894 TriU
669 903 TriU
656 911 TriU
645 919 TriU
635 926 TriU
627 932 TriU
619 938 TriU
613 943 TriU
607 948 TriU
601 952 TriU
2498 1747 TriU
1.000 UL
LT0
500 1683 M
23 -4 V
22 -5 V
23 -4 V
22 -4 V
23 -4 V
22 -4 V
23 -4 V
22 -4 V
23 -4 V
22 -3 V
23 -4 V
22 -3 V
23 -4 V
22 -3 V
23 -3 V
22 -3 V
23 -3 V
22 -3 V
23 -3 V
23 -3 V
22 -3 V
23 -2 V
22 -3 V
23 -2 V
22 -3 V
23 -2 V
22 -2 V
23 -2 V
22 -2 V
23 -2 V
22 -2 V
23 -2 V
22 -2 V
23 -1 V
22 -2 V
23 -2 V
22 -1 V
23 -1 V
22 -1 V
23 -2 V
23 -1 V
22 -1 V
23 0 V
22 -1 V
23 -1 V
22 -1 V
23 0 V
22 -1 V
23 0 V
22 0 V
23 0 V
22 -1 V
23 0 V
22 0 V
23 0 V
22 1 V
23 0 V
22 0 V
23 1 V
23 0 V
22 1 V
23 1 V
22 0 V
23 1 V
22 1 V
23 1 V
22 1 V
23 2 V
22 1 V
23 1 V
22 2 V
23 1 V
22 2 V
23 2 V
22 1 V
23 2 V
22 2 V
23 2 V
22 2 V
23 3 V
23 2 V
22 2 V
23 3 V
22 2 V
23 3 V
22 3 V
23 2 V
22 3 V
23 3 V
22 3 V
23 3 V
22 4 V
23 3 V
22 3 V
23 4 V
22 3 V
23 4 V
22 4 V
23 3 V
1.000 UL
LT0
500 1019 M
23 -17 V
22 -16 V
23 -16 V
22 -15 V
23 -14 V
22 -15 V
23 -13 V
22 -14 V
23 -13 V
22 -12 V
23 -12 V
22 -12 V
23 -11 V
22 -10 V
23 -10 V
22 -10 V
23 -9 V
22 -9 V
23 -8 V
23 -8 V
22 -8 V
23 -7 V
22 -6 V
23 -6 V
22 -6 V
23 -5 V
22 -5 V
23 -4 V
22 -4 V
23 -3 V
22 -3 V
23 -2 V
22 -2 V
23 -1 V
22 -1 V
23 -1 V
22 0 V
23 0 V
22 1 V
23 1 V
23 2 V
22 2 V
23 3 V
22 3 V
23 4 V
22 4 V
23 4 V
22 5 V
23 5 V
22 6 V
23 7 V
22 6 V
23 8 V
22 7 V
23 8 V
22 9 V
23 9 V
22 9 V
23 10 V
23 11 V
22 11 V
23 11 V
22 12 V
23 12 V
22 13 V
23 13 V
22 13 V
23 15 V
22 14 V
23 15 V
22 15 V
23 16 V
22 17 V
23 16 V
22 18 V
23 17 V
22 19 V
23 18 V
22 19 V
23 20 V
23 20 V
22 20 V
23 21 V
22 22 V
23 21 V
22 23 V
23 23 V
22 23 V
23 23 V
22 24 V
23 25 V
22 25 V
23 26 V
22 25 V
23 27 V
22 27 V
23 27 V
22 28 V
23 28 V
1.000 UL
LT0
500 1363 M
23 -2 V
22 -1 V
23 -1 V
22 -1 V
23 -1 V
22 -1 V
23 -1 V
22 -1 V
23 0 V
22 -1 V
23 -1 V
22 -1 V
23 -1 V
22 0 V
23 -1 V
22 -1 V
23 0 V
22 -1 V
23 -1 V
23 0 V
22 -1 V
23 0 V
22 0 V
23 -1 V
22 0 V
23 -1 V
22 0 V
23 0 V
22 0 V
23 -1 V
22 0 V
23 0 V
22 0 V
23 0 V
22 0 V
23 0 V
22 0 V
23 0 V
22 0 V
23 0 V
23 0 V
22 0 V
23 1 V
22 0 V
23 0 V
22 0 V
23 1 V
22 0 V
23 1 V
22 0 V
23 0 V
22 1 V
23 1 V
22 0 V
23 1 V
22 0 V
23 1 V
22 1 V
23 0 V
23 1 V
22 1 V
23 1 V
22 1 V
23 0 V
22 1 V
23 1 V
22 1 V
23 1 V
22 1 V
23 1 V
22 2 V
23 1 V
22 1 V
23 1 V
22 1 V
23 2 V
22 1 V
23 1 V
22 2 V
23 1 V
23 1 V
22 2 V
23 1 V
22 2 V
23 1 V
22 2 V
23 2 V
22 1 V
23 2 V
22 2 V
23 1 V
22 2 V
23 2 V
22 2 V
23 2 V
22 2 V
23 2 V
22 2 V
23 2 V
stroke
grestore
end
showpage
}}%
\put(2317,1747){\makebox(0,0)[r]{RO}}%
\put(2317,1847){\makebox(0,0)[r]{LRO}}%
\put(2317,1947){\makebox(0,0)[r]{SA}}%
\put(1615,50){\makebox(0,0){$1/N_{cop}$}}%
\put(100,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$<F_{max}>$}}%
\special{ps: currentpoint grestore moveto}%
}%
\put(2527,200){\makebox(0,0){1}}%
\put(2122,200){\makebox(0,0){0.8}}%
\put(1716,200){\makebox(0,0){0.6}}%
\put(1311,200){\makebox(0,0){0.4}}%
\put(905,200){\makebox(0,0){0.2}}%
\put(500,200){\makebox(0,0){0}}%
\put(450,1864){\makebox(0,0)[r]{0.798}}%
\put(450,1473){\makebox(0,0)[r]{0.796}}%
\put(450,1082){\makebox(0,0)[r]{0.794}}%
\put(450,691){\makebox(0,0)[r]{0.792}}%
\put(450,300){\makebox(0,0)[r]{0.79}}%
\end{picture}%
\endgroup
\endinput

fig2.tex
% GNUPLOT: LaTeX picture with Postscript
\begingroup%
  \makeatletter%
  \newcommand{\GNUPLOTspecial}{%
    \@sanitize\catcode`\%=14\relax\special}%
  \setlength{\unitlength}{0.1bp}%
{\GNUPLOTspecial{!
%!PS-Adobe-2.0 EPSF-2.0
%%Title: fm_vs_crr.tex
%%Creator: gnuplot 3.7 patchlevel 1
%%CreationDate: Thu Aug 17 22:50:05 2000
%%DocumentFonts: 
%%BoundingBox: 0 0 288 216
%%Orientation: Landscape
%%EndComments
/gnudict 256 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/userlinewidth gnulinewidth def
/vshift -33 def
/dl {10 mul} def
/hpt_ 31.5 def
/vpt_ 31.5 def
/hpt hpt_ def
/vpt vpt_ def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def
  /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke userlinewidth 2 mul setlinewidth } def
/AL { stroke userlinewidth 2 div setlinewidth } def
/UL { dup gnulinewidth mul /userlinewidth exch def
      10 mul /udl exch def } def
/PL { stroke userlinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 1 0 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 1 0 DL } def
/LT2 { PL [2 dl 3 dl] 0 0 1 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/Pnt { stroke [] 0 setdash
   gsave 1 setlinecap M 0 0 V stroke grestore } def
/Dia { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  Pnt } def
/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  Pnt } def
/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  Pnt  } def
/Star { 2 copy Pls Crs } def
/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V  hpt2 0 V  0 vpt2 V
  hpt2 neg 0 V  closepath fill } def
/TriUF { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath fill } def
/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke
  Pnt  } def
/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath fill} def
/DiaF { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath fill } def
/Pent { stroke [] 0 setdash 2 copy gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore Pnt } def
/PentF { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath fill grestore } def
/Circle { stroke [] 0 setdash 2 copy
  hpt 0 360 arc stroke Pnt } def
/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def
/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450  arc } bind def
/C1 { BL [] 0 setdash 2 copy        moveto
       2 copy  vpt 0 90 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C2 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C3 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C4 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C5 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 90 arc
       2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc } bind def
/C6 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 90 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C7 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 0 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C8 { BL [] 0 setdash 2 copy moveto
      2 copy vpt 270 360 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C9 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 270 450 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill
       2 copy moveto
       2 copy vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C11 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
       2 copy moveto
       2 copy  vpt 270 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C12 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C13 { BL [] 0 setdash  2 copy moveto
       2 copy  vpt 0 90 arc closepath fill
       2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C14 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 360 arc closepath fill
               vpt 0 360 arc } bind def
/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/Rec   { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
       neg 0 rlineto closepath } bind def
/Square { dup Rec } bind def
/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def
/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def
/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def
/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def
/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill
       exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill
       2 copy vpt Square fill
       Bsquare } bind def
/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def
/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill
       Bsquare } bind def
/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill
       Bsquare } bind def
/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def
/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy vpt Square fill Bsquare } bind def
/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def
/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def
/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def
/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def
/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def
/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def
/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def
/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def
/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def
/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def
/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def
/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def
/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def
/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def
/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def
/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def
/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def
/DiaE { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke } def
/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke } def
/TriUE { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke } def
/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke } def
/PentE { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore } def
/CircE { stroke [] 0 setdash 
  hpt 0 360 arc stroke } def
/Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def
/DiaW { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V Opaque stroke } def
/BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V Opaque stroke } def
/TriUW { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V Opaque stroke } def
/TriDW { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V Opaque stroke } def
/PentW { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  Opaque stroke grestore } def
/CircW { stroke [] 0 setdash 
  hpt 0 360 arc Opaque stroke } def
/BoxFill { gsave Rec 1 setgray fill grestore } def
end
%%EndProlog
}}%
\begin{picture}(2880,2160)(0,0)%
{\GNUPLOTspecial{"
gnudict begin
gsave
0 0 translate
0.100 0.100 scale
0 setgray
newpath
1.000 UL
LTb
400 300 M
63 0 V
2267 0 R
-63 0 V
400 551 M
63 0 V
2267 0 R
-63 0 V
400 803 M
63 0 V
2267 0 R
-63 0 V
400 1054 M
63 0 V
2267 0 R
-63 0 V
400 1306 M
63 0 V
2267 0 R
-63 0 V
400 1557 M
63 0 V
2267 0 R
-63 0 V
400 1809 M
63 0 V
2267 0 R
-63 0 V
400 2060 M
63 0 V
2267 0 R
-63 0 V
400 300 M
0 63 V
0 1697 R
0 -63 V
866 300 M
0 63 V
0 1697 R
0 -63 V
1332 300 M
0 63 V
0 1697 R
0 -63 V
1798 300 M
0 63 V
0 1697 R
0 -63 V
2264 300 M
0 63 V
0 1697 R
0 -63 V
2730 300 M
0 63 V
0 1697 R
0 -63 V
1.000 UL
LTb
400 300 M
2330 0 V
0 1760 V
-2330 0 V
400 300 L
1.000 UP
1.000 UL
LT0
2367 1947 M
263 0 V
-263 31 R
0 -62 V
263 62 R
0 -62 V
696 1753 M
0 290 V
665 1753 M
62 0 V
-62 290 R
62 0 V
697 -746 R
0 320 V
-31 -320 R
62 0 V
-62 320 R
62 0 V
323 -552 R
0 354 V
-31 -354 R
62 0 V
-62 354 R
62 0 V
2003 924 M
0 382 V
1972 924 M
62 0 V
-62 382 R
62 0 V
2166 829 M
0 410 V
2135 829 M
62 0 V
-62 410 R
62 0 V
93 -481 R
0 441 V
2259 758 M
62 0 V
-62 441 R
62 0 V
62 -504 R
0 474 V
2352 695 M
62 0 V
-62 474 R
62 0 V
696 1898 BoxF
1424 1457 BoxF
1778 1242 BoxF
2003 1115 BoxF
2166 1034 BoxF
2290 978 BoxF
2383 932 BoxF
2498 1947 BoxF
1.000 UP
1.000 UL
LT0
2367 1847 M
263 0 V
-263 31 R
0 -62 V
263 62 R
0 -62 V
696 712 M
0 108 V
665 712 M
62 0 V
665 820 M
62 0 V
1424 609 M
0 111 V
1393 609 M
62 0 V
-62 111 R
62 0 V
1778 554 M
0 113 V
1747 554 M
62 0 V
-62 113 R
62 0 V
2003 516 M
0 115 V
1972 516 M
62 0 V
-62 115 R
62 0 V
2166 488 M
0 116 V
2135 488 M
62 0 V
-62 116 R
62 0 V
93 -137 R
0 120 V
2259 467 M
62 0 V
-62 120 R
62 0 V
62 -134 R
0 123 V
2352 453 M
62 0 V
-62 123 R
62 0 V
696 766 Box
1424 665 Box
1778 611 Box
2003 573 Box
2166 546 Box
2290 527 Box
2383 514 Box
2498 1847 Box
1.000 UL
LT0
400 832 M
24 -4 V
23 -4 V
24 -4 V
23 -3 V
24 -4 V
23 -4 V
24 -4 V
23 -4 V
24 -3 V
23 -4 V
24 -4 V
23 -4 V
24 -3 V
23 -4 V
24 -4 V
24 -4 V
23 -4 V
24 -3 V
23 -4 V
24 -4 V
23 -4 V
24 -4 V
23 -3 V
24 -4 V
23 -4 V
24 -4 V
23 -4 V
24 -3 V
24 -4 V
23 -4 V
24 -4 V
23 -4 V
24 -3 V
23 -4 V
24 -4 V
23 -4 V
24 -3 V
23 -4 V
24 -4 V
23 -4 V
24 -4 V
23 -3 V
24 -4 V
24 -4 V
23 -4 V
24 -4 V
23 -3 V
24 -4 V
23 -4 V
24 -4 V
23 -4 V
24 -3 V
23 -4 V
24 -4 V
23 -4 V
24 -3 V
24 -4 V
23 -4 V
24 -4 V
23 -4 V
24 -3 V
23 -4 V
24 -4 V
23 -4 V
24 -4 V
23 -3 V
24 -4 V
23 -4 V
24 -4 V
23 -4 V
24 -3 V
24 -4 V
23 -4 V
24 -4 V
23 -3 V
24 -4 V
23 -4 V
24 -4 V
23 -4 V
24 -3 V
23 -4 V
24 -4 V
23 -4 V
24 -4 V
24 -3 V
23 -4 V
24 -4 V
23 -4 V
24 -4 V
23 -3 V
24 -4 V
23 -4 V
24 -4 V
23 -3 V
24 -4 V
23 -4 V
24 -4 V
23 -4 V
24 -3 V
1.000 UL
LT0
400 1942 M
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -13 V
23 -12 V
24 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -13 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -13 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
24 -12 V
23 -13 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
23 -12 V
24 -12 V
stroke
grestore
end
showpage
}}%
\put(2317,1847){\makebox(0,0)[r]{$<\rho>$}}%
\put(2317,1947){\makebox(0,0)[r]{$\chi_{Z(2)}(5,5)$}}%
\put(1565,50){\makebox(0,0){$<F_{max}>$}}%
\put(2730,200){\makebox(0,0){0.7786}}%
\put(2264,200){\makebox(0,0){0.7785}}%
\put(1798,200){\makebox(0,0){0.7784}}%
\put(1332,200){\makebox(0,0){0.7783}}%
\put(866,200){\makebox(0,0){0.7782}}%
\put(400,200){\makebox(0,0){0.7781}}%
\put(350,2060){\makebox(0,0)[r]{0.05}}%
\put(350,1809){\makebox(0,0)[r]{0.049}}%
\put(350,1557){\makebox(0,0)[r]{0.048}}%
\put(350,1306){\makebox(0,0)[r]{0.047}}%
\put(350,1054){\makebox(0,0)[r]{0.046}}%
\put(350,803){\makebox(0,0)[r]{0.045}}%
\put(350,551){\makebox(0,0)[r]{0.044}}%
\put(350,300){\makebox(0,0)[r]{0.043}}%
\end{picture}%
\endgroup
\endinput

fig3.tex
% GNUPLOT: LaTeX picture with Postscript
\begingroup%
  \makeatletter%
  \newcommand{\GNUPLOTspecial}{%
    \@sanitize\catcode`\%=14\relax\special}%
  \setlength{\unitlength}{0.1bp}%
{\GNUPLOTspecial{!
%!PS-Adobe-2.0 EPSF-2.0
%%Title: dens20_new.tex
%%Creator: gnuplot 3.7 patchlevel 1
%%CreationDate: Thu Aug 17 23:51:16 2000
%%DocumentFonts: 
%%BoundingBox: 0 0 288 216
%%Orientation: Landscape
%%EndComments
/gnudict 256 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/userlinewidth gnulinewidth def
/vshift -33 def
/dl {10 mul} def
/hpt_ 31.5 def
/vpt_ 31.5 def
/hpt hpt_ def
/vpt vpt_ def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def
  /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke userlinewidth 2 mul setlinewidth } def
/AL { stroke userlinewidth 2 div setlinewidth } def
/UL { dup gnulinewidth mul /userlinewidth exch def
      10 mul /udl exch def } def
/PL { stroke userlinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 1 0 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 1 0 DL } def
/LT2 { PL [2 dl 3 dl] 0 0 1 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/Pnt { stroke [] 0 setdash
   gsave 1 setlinecap M 0 0 V stroke grestore } def
/Dia { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  Pnt } def
/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  Pnt } def
/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  Pnt  } def
/Star { 2 copy Pls Crs } def
/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V  hpt2 0 V  0 vpt2 V
  hpt2 neg 0 V  closepath fill } def
/TriUF { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath fill } def
/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke
  Pnt  } def
/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath fill} def
/DiaF { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath fill } def
/Pent { stroke [] 0 setdash 2 copy gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore Pnt } def
/PentF { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath fill grestore } def
/Circle { stroke [] 0 setdash 2 copy
  hpt 0 360 arc stroke Pnt } def
/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def
/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450  arc } bind def
/C1 { BL [] 0 setdash 2 copy        moveto
       2 copy  vpt 0 90 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C2 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C3 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C4 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C5 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 90 arc
       2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc } bind def
/C6 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 90 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C7 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 0 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C8 { BL [] 0 setdash 2 copy moveto
      2 copy vpt 270 360 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C9 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 270 450 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill
       2 copy moveto
       2 copy vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C11 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
       2 copy moveto
       2 copy  vpt 270 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C12 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C13 { BL [] 0 setdash  2 copy moveto
       2 copy  vpt 0 90 arc closepath fill
       2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C14 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 360 arc closepath fill
               vpt 0 360 arc } bind def
/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/Rec   { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
       neg 0 rlineto closepath } bind def
/Square { dup Rec } bind def
/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def
/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def
/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def
/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def
/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill
       exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill
       2 copy vpt Square fill
       Bsquare } bind def
/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def
/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill
       Bsquare } bind def
/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill
       Bsquare } bind def
/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def
/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy vpt Square fill Bsquare } bind def
/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def
/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def
/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def
/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def
/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def
/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def
/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def
/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def
/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def
/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def
/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def
/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def
/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def
/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def
/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def
/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def
/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def
/DiaE { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke } def
/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke } def
/TriUE { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke } def
/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke } def
/PentE { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore } def
/CircE { stroke [] 0 setdash 
  hpt 0 360 arc stroke } def
/Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def
/DiaW { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V Opaque stroke } def
/BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V Opaque stroke } def
/TriUW { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V Opaque stroke } def
/TriDW { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V Opaque stroke } def
/PentW { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  Opaque stroke grestore } def
/CircW { stroke [] 0 setdash 
  hpt 0 360 arc Opaque stroke } def
/BoxFill { gsave Rec 1 setgray fill grestore } def
end
%%EndProlog
}}%
\begin{picture}(2880,2160)(0,0)%
{\GNUPLOTspecial{"
gnudict begin
gsave
0 0 translate
0.100 0.100 scale
0 setgray
newpath
1.000 UL
LTb
450 460 M
63 0 V
2217 0 R
-63 0 V
450 780 M
63 0 V
2217 0 R
-63 0 V
450 1100 M
63 0 V
2217 0 R
-63 0 V
450 1420 M
63 0 V
2217 0 R
-63 0 V
450 1740 M
63 0 V
2217 0 R
-63 0 V
450 2060 M
63 0 V
2217 0 R
-63 0 V
493 300 M
0 63 V
0 1697 R
0 -63 V
919 300 M
0 63 V
0 1697 R
0 -63 V
1345 300 M
0 63 V
0 1697 R
0 -63 V
1771 300 M
0 63 V
0 1697 R
0 -63 V
2197 300 M
0 63 V
0 1697 R
0 -63 V
2623 300 M
0 63 V
0 1697 R
0 -63 V
1.000 UL
LTb
450 300 M
2280 0 V
0 1760 V
-2280 0 V
450 300 L
0.800 UP
1.000 UL
LT0
1400 1947 M
250 0 V
-250 31 R
0 -62 V
250 62 R
0 -62 V
2623 671 M
0 89 V
-31 -89 R
62 0 V
-62 89 R
62 0 V
1558 584 M
0 90 V
-31 -90 R
62 0 V
-62 90 R
62 0 V
1203 538 M
0 90 V
-31 -90 R
62 0 V
-62 90 R
62 0 V
1025 508 M
0 90 V
994 508 M
62 0 V
-62 90 R
62 0 V
919 485 M
0 91 V
888 485 M
62 0 V
-62 91 R
62 0 V
848 468 M
0 92 V
817 468 M
62 0 V
-62 92 R
62 0 V
797 455 M
0 94 V
766 455 M
62 0 V
-62 94 R
62 0 V
2623 715 Box
1558 629 Box
1203 583 Box
1025 553 Box
919 530 Box
848 514 Box
797 502 Box
1525 1947 Box
0.800 UP
1.000 UL
LT0
1400 1847 M
250 0 V
-250 31 R
0 -62 V
250 62 R
0 -62 V
2623 702 M
0 73 V
-31 -73 R
62 0 V
-62 73 R
62 0 V
1558 645 M
0 74 V
-31 -74 R
62 0 V
-62 74 R
62 0 V
1203 610 M
0 77 V
-31 -77 R
62 0 V
-62 77 R
62 0 V
1025 590 M
0 81 V
994 590 M
62 0 V
-62 81 R
62 0 V
2623 739 BoxF
1558 682 BoxF
1203 649 BoxF
1025 630 BoxF
1525 1847 BoxF
0.800 UP
1.000 UL
LT0
1400 1747 M
250 0 V
-250 31 R
0 -62 V
250 62 R
0 -62 V
973 -168 R
0 143 V
-31 -143 R
62 0 V
-62 143 R
62 0 V
1558 1325 M
0 149 V
-31 -149 R
62 0 V
-62 149 R
62 0 V
1203 1208 M
0 150 V
-31 -150 R
62 0 V
-62 150 R
62 0 V
1025 1131 M
0 150 V
994 1131 M
62 0 V
-62 150 R
62 0 V
919 1078 M
0 150 V
888 1078 M
62 0 V
-62 150 R
62 0 V
848 1037 M
0 154 V
817 1037 M
62 0 V
-62 154 R
62 0 V
797 1006 M
0 159 V
766 1006 M
62 0 V
-62 159 R
62 0 V
2623 1619 Circle
1558 1400 Circle
1203 1283 Circle
1025 1206 Circle
919 1153 Circle
848 1114 Circle
797 1086 Circle
1525 1747 Circle
0.800 UP
1.000 UL
LT0
1400 1647 M
250 0 V
-250 31 R
0 -62 V
250 62 R
0 -62 V
973 -116 R
0 180 V
-31 -180 R
62 0 V
-62 180 R
62 0 V
1558 1326 M
0 182 V
-31 -182 R
62 0 V
-62 182 R
62 0 V
1203 1243 M
0 185 V
-31 -185 R
62 0 V
-62 185 R
62 0 V
1025 1189 M
0 188 V
994 1189 M
62 0 V
-62 188 R
62 0 V
919 1150 M
0 192 V
888 1150 M
62 0 V
-62 192 R
62 0 V
848 1120 M
0 197 V
817 1120 M
62 0 V
-62 197 R
62 0 V
797 1093 M
0 201 V
766 1093 M
62 0 V
-62 201 R
62 0 V
2623 1590 CircleF
1558 1417 CircleF
1203 1336 CircleF
1025 1283 CircleF
919 1246 CircleF
848 1218 CircleF
797 1194 CircleF
1525 1647 CircleF
1.000 UL
LT0
450 398 M
23 7 V
23 7 V
23 8 V
23 7 V
23 6 V
23 7 V
23 7 V
23 7 V
23 6 V
23 6 V
23 7 V
23 6 V
23 6 V
23 6 V
23 6 V
23 5 V
24 6 V
23 5 V
23 6 V
23 5 V
23 5 V
23 5 V
23 5 V
23 5 V
23 5 V
23 5 V
23 4 V
23 5 V
23 4 V
23 4 V
23 4 V
23 4 V
23 4 V
23 4 V
23 4 V
23 3 V
23 4 V
23 3 V
23 4 V
23 3 V
23 3 V
23 3 V
23 3 V
23 2 V
23 3 V
23 3 V
23 2 V
23 2 V
23 2 V
24 3 V
23 2 V
23 1 V
23 2 V
23 2 V
23 1 V
23 2 V
23 1 V
23 2 V
23 1 V
23 1 V
23 1 V
23 0 V
23 1 V
23 1 V
23 0 V
23 1 V
23 0 V
23 0 V
23 0 V
23 0 V
23 0 V
23 0 V
23 -1 V
23 0 V
23 -1 V
23 0 V
23 -1 V
23 -1 V
23 -1 V
23 -1 V
23 -1 V
23 -2 V
24 -1 V
23 -2 V
23 -1 V
23 -2 V
23 -2 V
23 -2 V
23 -2 V
23 -2 V
23 -2 V
23 -3 V
23 -2 V
23 -3 V
23 -3 V
23 -2 V
23 -3 V
23 -3 V
23 -3 V
1.000 UL
LT0
450 862 M
23 17 V
23 16 V
23 16 V
23 16 V
23 15 V
23 15 V
23 15 V
23 15 V
23 15 V
23 14 V
23 15 V
23 14 V
23 13 V
23 14 V
23 13 V
23 13 V
24 13 V
23 13 V
23 12 V
23 12 V
23 12 V
23 12 V
23 11 V
23 12 V
23 11 V
23 11 V
23 10 V
23 11 V
23 10 V
23 10 V
23 10 V
23 9 V
23 9 V
23 9 V
23 9 V
23 9 V
23 8 V
23 8 V
23 8 V
23 8 V
23 8 V
23 7 V
23 7 V
23 7 V
23 6 V
23 7 V
23 6 V
23 6 V
23 6 V
24 5 V
23 5 V
23 5 V
23 5 V
23 5 V
23 4 V
23 4 V
23 4 V
23 4 V
23 4 V
23 3 V
23 3 V
23 3 V
23 2 V
23 3 V
23 2 V
23 2 V
23 1 V
23 2 V
23 1 V
23 1 V
23 1 V
23 1 V
23 0 V
23 0 V
23 0 V
23 0 V
23 -1 V
23 0 V
23 -1 V
23 -2 V
23 -1 V
23 -2 V
24 -2 V
23 -2 V
23 -2 V
23 -2 V
23 -3 V
23 -3 V
23 -3 V
23 -4 V
23 -3 V
23 -4 V
23 -4 V
23 -5 V
23 -4 V
23 -5 V
23 -5 V
23 -5 V
23 -6 V
1.000 UL
LT0
450 1033 M
23 12 V
23 12 V
23 12 V
23 11 V
23 12 V
23 11 V
23 11 V
23 11 V
23 10 V
23 11 V
23 10 V
23 10 V
23 10 V
23 10 V
23 10 V
23 9 V
24 9 V
23 9 V
23 9 V
23 9 V
23 9 V
23 8 V
23 8 V
23 8 V
23 8 V
23 8 V
23 8 V
23 7 V
23 7 V
23 7 V
23 7 V
23 7 V
23 6 V
23 7 V
23 6 V
23 6 V
23 6 V
23 5 V
23 6 V
23 5 V
23 5 V
23 5 V
23 5 V
23 5 V
23 4 V
23 4 V
23 5 V
23 4 V
23 3 V
24 4 V
23 3 V
23 4 V
23 3 V
23 3 V
23 2 V
23 3 V
23 2 V
23 3 V
23 2 V
23 2 V
23 1 V
23 2 V
23 1 V
23 1 V
23 1 V
23 1 V
23 1 V
23 1 V
23 0 V
23 0 V
23 0 V
23 0 V
23 0 V
23 -1 V
23 -1 V
23 0 V
23 -1 V
23 -2 V
23 -1 V
23 -2 V
23 -1 V
23 -2 V
24 -2 V
23 -2 V
23 -3 V
23 -2 V
23 -3 V
23 -3 V
23 -3 V
23 -3 V
23 -4 V
23 -3 V
23 -4 V
23 -4 V
23 -4 V
23 -4 V
23 -5 V
23 -4 V
23 -5 V
1.000 UL
LT0
450 576 M
23 2 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
24 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
24 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
24 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 2 V
23 3 V
23 2 V
23 2 V
23 2 V
23 2 V
23 3 V
stroke
grestore
end
showpage
}}%
\put(1350,1647){\makebox(0,0)[r]{$L=24,~~~"~"~~~$}}%
\put(1350,1747){\makebox(0,0)[r]{$L=20, \beta=2.5$}}%
\put(1350,1847){\makebox(0,0)[r]{$L=24,~~~"~"~~~$}}%
\put(1350,1947){\makebox(0,0)[r]{$L=20, \beta=2.4$}}%
\put(1590,50){\makebox(0,0){$1/N_{cop}$}}%
\put(100,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$<\rho>/\sigma_{SU(2)}\cdot a^2$}}%
\special{ps: currentpoint grestore moveto}%
}%
\put(2623,200){\makebox(0,0){1}}%
\put(2197,200){\makebox(0,0){0.8}}%
\put(1771,200){\makebox(0,0){0.6}}%
\put(1345,200){\makebox(0,0){0.4}}%
\put(919,200){\makebox(0,0){0.2}}%
\put(493,200){\makebox(0,0){0}}%
\put(400,2060){\makebox(0,0)[r]{0.7}}%
\put(400,1740){\makebox(0,0)[r]{0.68}}%
\put(400,1420){\makebox(0,0)[r]{0.66}}%
\put(400,1100){\makebox(0,0)[r]{0.64}}%
\put(400,780){\makebox(0,0)[r]{0.62}}%
\put(400,460){\makebox(0,0)[r]{0.6}}%
\end{picture}%
\endgroup
\endinput

fig4.tex
% GNUPLOT: LaTeX picture with Postscript
\begingroup%
  \makeatletter%
  \newcommand{\GNUPLOTspecial}{%
    \@sanitize\catcode`\%=14\relax\special}%
  \setlength{\unitlength}{0.1bp}%
{\GNUPLOTspecial{!
%!PS-Adobe-2.0 EPSF-2.0
%%Title: crr_all_24.tex
%%Creator: gnuplot 3.7 patchlevel 1
%%CreationDate: Fri Aug 11 12:14:14 2000
%%DocumentFonts:
%%BoundingBox: 0 0 288 216
%%Orientation: Landscape
%%EndComments
/gnudict 256 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/userlinewidth gnulinewidth def
/vshift -33 def
/dl {10 mul} def
/hpt_ 31.5 def
/vpt_ 31.5 def
/hpt hpt_ def
/vpt vpt_ def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def
  /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke userlinewidth 2 mul setlinewidth } def
/AL { stroke userlinewidth 2 div setlinewidth } def
/UL { dup gnulinewidth mul /userlinewidth exch def
      10 mul /udl exch def } def
/PL { stroke userlinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 1 0 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 1 0 DL } def
/LT2 { PL [2 dl 3 dl] 0 0 1 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/Pnt { stroke [] 0 setdash
   gsave 1 setlinecap M 0 0 V stroke grestore } def
/Dia { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  Pnt } def
/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  Pnt } def
/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  Pnt  } def
/Star { 2 copy Pls Crs } def
/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V  hpt2 0 V  0 vpt2 V
  hpt2 neg 0 V  closepath fill } def
/TriUF { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath fill } def
/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke
  Pnt  } def
/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath fill} def
/DiaF { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath fill } def
/Pent { stroke [] 0 setdash 2 copy gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore Pnt } def
/PentF { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath fill grestore } def
/Circle { stroke [] 0 setdash 2 copy
  hpt 0 360 arc stroke Pnt } def
/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def
/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450  arc } bind def
/C1 { BL [] 0 setdash 2 copy        moveto
       2 copy  vpt 0 90 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C2 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C3 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C4 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C5 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 90 arc
       2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc } bind def
/C6 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 90 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C7 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 0 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C8 { BL [] 0 setdash 2 copy moveto
      2 copy vpt 270 360 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C9 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 270 450 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill
       2 copy moveto
       2 copy vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C11 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
       2 copy moveto
       2 copy  vpt 270 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C12 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C13 { BL [] 0 setdash  2 copy moveto
       2 copy  vpt 0 90 arc closepath fill
       2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C14 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 360 arc closepath fill
               vpt 0 360 arc } bind def
/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/Rec   { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
       neg 0 rlineto closepath } bind def
/Square { dup Rec } bind def
/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def
/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def
/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def
/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def
/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill
       exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill
       2 copy vpt Square fill
       Bsquare } bind def
/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def
/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill
       Bsquare } bind def
/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill
       Bsquare } bind def
/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def
/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy vpt Square fill Bsquare } bind def
/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def
/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def
/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def
/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def
/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def
/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def
/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def
/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def
/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def
/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def
/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def
/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def
/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def
/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def
/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def
/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def
/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def
/DiaE { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke } def
/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke } def
/TriUE { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke } def
/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke } def
/PentE { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore } def
/CircE { stroke [] 0 setdash
  hpt 0 360 arc stroke } def
/Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def
/DiaW { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V Opaque stroke } def
/BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V Opaque stroke } def
/TriUW { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V Opaque stroke } def
/TriDW { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V Opaque stroke } def
/PentW { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  Opaque stroke grestore } def
/CircW { stroke [] 0 setdash
  hpt 0 360 arc Opaque stroke } def
/BoxFill { gsave Rec 1 setgray fill grestore } def
end
%%EndProlog
}}%
\begin{picture}(2880,2160)(0,0)%
{\GNUPLOTspecial{"
gnudict begin
gsave
0 0 translate
0.100 0.100 scale
0 setgray
newpath
1.000 UL
LTb
500 300 M
63 0 V
2167 0 R
-63 0 V
500 551 M
63 0 V
2167 0 R
-63 0 V
500 803 M
63 0 V
2167 0 R
-63 0 V
500 1054 M
63 0 V
2167 0 R
-63 0 V
500 1306 M
63 0 V
2167 0 R
-63 0 V
500 1557 M
63 0 V
2167 0 R
-63 0 V
500 1809 M
63 0 V
2167 0 R
-63 0 V
500 2060 M
63 0 V
2167 0 R
-63 0 V
562 300 M
0 63 V
0 1697 R
0 -63 V
872 300 M
0 63 V
0 1697 R
0 -63 V
1181 300 M
0 63 V
0 1697 R
0 -63 V
1491 300 M
0 63 V
0 1697 R
0 -63 V
1801 300 M
0 63 V
0 1697 R
0 -63 V
2111 300 M
0 63 V
0 1697 R
0 -63 V
2420 300 M
0 63 V
0 1697 R
0 -63 V
2730 300 M
0 63 V
0 1697 R
0 -63 V
1.000 UL
LTb
500 300 M
2230 0 V
0 1760 V
-2230 0 V
500 300 L
0.800 UP
1.000 UL
LT0
900 1947 M
250 0 V
-250 31 R
0 -62 V
250 62 R
0 -62 V
976 -471 R
0 141 V
-31 -141 R
62 0 V
-62 141 R
62 0 V
1610 1375 M
0 148 V
-31 -148 R
62 0 V
-62 148 R
62 0 V
1352 1340 M
0 152 V
-31 -152 R
62 0 V
-62 152 R
62 0 V
577 1224 M
0 176 V
546 1224 M
62 0 V
-62 176 R
62 0 V
2126 1515 BoxF
1610 1449 BoxF
1352 1416 BoxF
577 1312 BoxF
1025 1947 BoxF
0.800 UP
1.000 UL
LT0
900 1847 M
250 0 V
-250 31 R
0 -62 V
250 62 R
0 -62 V
945 -403 R
0 130 V
-31 -130 R
62 0 V
-62 130 R
62 0 V
1579 1318 M
0 142 V
-31 -142 R
62 0 V
-62 142 R
62 0 V
1321 1254 M
0 153 V
-31 -153 R
62 0 V
-62 153 R
62 0 V
1166 1207 M
0 165 V
-31 -165 R
62 0 V
-62 165 R
62 0 V
1063 1171 M
0 178 V
-31 -178 R
62 0 V
-62 178 R
62 0 V
989 1143 M
0 192 V
958 1143 M
62 0 V
-62 192 R
62 0 V
546 986 M
0 202 V
515 986 M
62 0 V
-62 202 R
62 0 V
2095 1478 Box
1579 1389 Box
1321 1331 Box
1166 1290 Box
1063 1260 Box
989 1239 Box
546 1087 Box
1025 1847 Box
0.800 UP
1.000 UL
LT0
900 1747 M
250 0 V
-250 31 R
0 -62 V
250 62 R
0 -62 V
961 -205 R
0 145 V
-31 -145 R
62 0 V
-62 145 R
62 0 V
1594 1409 M
0 158 V
-31 -158 R
62 0 V
-62 158 R
62 0 V
1336 1346 M
0 172 V
-31 -172 R
62 0 V
-62 172 R
62 0 V
1181 1301 M
0 186 V
-31 -186 R
62 0 V
-62 186 R
62 0 V
1078 1263 M
0 201 V
-31 -201 R
62 0 V
-62 201 R
62 0 V
1004 1230 M
0 216 V
973 1230 M
62 0 V
-62 216 R
62 0 V
562 1067 M
0 201 V
531 1067 M
62 0 V
-62 201 R
62 0 V
2111 1584 Circle
1594 1488 Circle
1336 1432 Circle
1181 1394 Circle
1078 1364 Circle
1004 1338 Circle
562 1167 Circle
1025 1747 Circle
0.800 UP
1.000 UL
LT0
900 1647 M
250 0 V
-250 31 R
0 -62 V
250 62 R
0 -62 V
961 -355 R
0 219 V
-31 -219 R
62 0 V
-62 219 R
62 0 V
1594 1080 M
0 231 V
-31 -231 R
62 0 V
-62 231 R
62 0 V
1336 961 M
0 240 V
1305 961 M
62 0 V
-62 240 R
62 0 V
1181 872 M
0 248 V
1150 872 M
62 0 V
-62 248 R
62 0 V
1078 801 M
0 256 V
1047 801 M
62 0 V
-62 256 R
62 0 V
1004 743 M
0 263 V
973 743 M
62 0 V
-62 263 R
62 0 V
949 695 M
0 270 V
918 695 M
62 0 V
918 965 M
62 0 V
906 655 M
0 276 V
875 655 M
62 0 V
875 931 M
62 0 V
872 620 M
0 284 V
841 620 M
62 0 V
841 904 M
62 0 V
562 325 M
0 277 V
531 325 M
62 0 V
531 602 M
62 0 V
2111 1370 CircleF
1594 1195 CircleF
1336 1081 CircleF
1181 996 CircleF
1078 929 CircleF
1004 875 CircleF
949 830 CircleF
906 793 CircleF
872 762 CircleF
562 463 CircleF
1025 1647 CircleF
1.000 UL
LT0
500 395 M
23 25 V
22 25 V
23 25 V
22 24 V
23 24 V
22 23 V
23 23 V
22 23 V
23 22 V
22 22 V
23 22 V
22 21 V
23 21 V
22 20 V
23 20 V
22 20 V
23 19 V
22 19 V
23 19 V
23 18 V
22 18 V
23 18 V
22 17 V
23 17 V
22 16 V
23 16 V
22 16 V
23 15 V
22 15 V
23 14 V
22 14 V
23 14 V
22 14 V
23 13 V
22 12 V
23 12 V
22 12 V
23 12 V
22 11 V
23 11 V
23 10 V
22 10 V
23 10 V
22 9 V
23 9 V
22 9 V
23 8 V
22 8 V
23 7 V
22 7 V
23 7 V
22 6 V
23 6 V
22 6 V
23 5 V
22 5 V
23 4 V
22 5 V
23 3 V
23 4 V
22 3 V
23 2 V
22 2 V
23 2 V
22 2 V
23 1 V
22 1 V
23 0 V
22 0 V
23 0 V
22 -1 V
23 -1 V
22 -2 V
23 -1 V
22 -3 V
23 -2 V
22 -3 V
23 -4 V
22 -3 V
23 -4 V
23 -5 V
22 -5 V
23 -5 V
22 -5 V
23 -6 V
22 -7 V
23 -6 V
22 -7 V
23 -8 V
22 -8 V
23 -8 V
22 -8 V
23 -9 V
22 -10 V
23 -9 V
22 -10 V
23 -11 V
22 -11 V
23 -11 V
1.000 UL
LT0
500 1147 M
23 9 V
22 10 V
23 10 V
22 10 V
23 9 V
22 9 V
23 10 V
22 9 V
23 9 V
22 8 V
23 9 V
22 9 V
23 8 V
22 9 V
23 8 V
22 8 V
23 8 V
22 8 V
23 7 V
23 8 V
22 8 V
23 7 V
22 7 V
23 7 V
22 7 V
23 7 V
22 7 V
23 7 V
22 6 V
23 6 V
22 7 V
23 6 V
22 6 V
23 6 V
22 5 V
23 6 V
22 6 V
23 5 V
22 5 V
23 6 V
23 5 V
22 4 V
23 5 V
22 5 V
23 4 V
22 5 V
23 4 V
22 4 V
23 4 V
22 4 V
23 4 V
22 4 V
23 3 V
22 4 V
23 3 V
22 3 V
23 4 V
22 2 V
23 3 V
23 3 V
22 3 V
23 2 V
22 2 V
23 3 V
22 2 V
23 2 V
22 2 V
23 1 V
22 2 V
23 1 V
22 2 V
23 1 V
22 1 V
23 1 V
22 1 V
23 1 V
22 0 V
23 1 V
22 0 V
23 0 V
23 1 V
22 0 V
23 0 V
22 -1 V
23 0 V
22 -1 V
23 0 V
22 -1 V
23 -1 V
22 -1 V
23 -1 V
22 -1 V
23 -1 V
22 -2 V
23 -1 V
22 -2 V
23 -2 V
22 -2 V
23 -2 V
1.000 UL
LT0
500 1064 M
23 8 V
22 9 V
23 9 V
22 8 V
23 8 V
22 9 V
23 8 V
22 8 V
23 8 V
22 8 V
23 8 V
22 8 V
23 7 V
22 8 V
23 8 V
22 7 V
23 7 V
22 8 V
23 7 V
23 7 V
22 7 V
23 7 V
22 7 V
23 7 V
22 6 V
23 7 V
22 6 V
23 7 V
22 6 V
23 6 V
22 6 V
23 7 V
22 6 V
23 5 V
22 6 V
23 6 V
22 6 V
23 5 V
22 6 V
23 5 V
23 5 V
22 6 V
23 5 V
22 5 V
23 5 V
22 5 V
23 4 V
22 5 V
23 5 V
22 4 V
23 5 V
22 4 V
23 4 V
22 5 V
23 4 V
22 4 V
23 4 V
22 4 V
23 3 V
23 4 V
22 4 V
23 3 V
22 4 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 2 V
23 3 V
22 2 V
23 2 V
22 3 V
23 2 V
22 2 V
23 2 V
23 2 V
22 2 V
23 1 V
22 2 V
23 1 V
22 2 V
23 1 V
22 2 V
23 1 V
22 1 V
23 1 V
22 1 V
23 1 V
22 0 V
23 1 V
22 1 V
23 0 V
22 1 V
23 0 V
1.000 UL
LT0
500 1305 M
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 2 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 2 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 2 V
23 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 2 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 2 V
22 3 V
23 3 V
22 3 V
23 3 V
22 3 V
23 2 V
23 3 V
22 3 V
23 3 V
22 3 V
23 3 V
22 2 V
23 3 V
22 3 V
23 3 V
22 3 V
23 2 V
22 3 V
23 3 V
22 3 V
23 3 V
22 2 V
23 3 V
22 3 V
23 3 V
stroke
grestore
end
showpage
}}%
\put(850,1647){\makebox(0,0)[r]{  L=12}}%
\put(850,1747){\makebox(0,0)[r]{  L=16}}%
\put(850,1847){\makebox(0,0)[r]{  L=20}}%
\put(850,1947){\makebox(0,0)[r]{  L=24}}%
\put(1615,50){\makebox(0,0){$1/N_{cop}$}}%
\put(100,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$\chi_{Z(2)}(4,4)$}}%
\special{ps: currentpoint grestore moveto}%
}%
\put(2730,200){\makebox(0,0){0.7}}%
\put(2420,200){\makebox(0,0){0.6}}%
\put(2111,200){\makebox(0,0){0.5}}%
\put(1801,200){\makebox(0,0){0.4}}%
\put(1491,200){\makebox(0,0){0.3}}%
\put(1181,200){\makebox(0,0){0.2}}%
\put(872,200){\makebox(0,0){0.1}}%
\put(562,200){\makebox(0,0){0}}%
\put(450,2060){\makebox(0,0)[r]{0.05}}%
\put(450,1809){\makebox(0,0)[r]{0.048}}%
\put(450,1557){\makebox(0,0)[r]{0.046}}%
\put(450,1306){\makebox(0,0)[r]{0.044}}%
\put(450,1054){\makebox(0,0)[r]{0.042}}%
\put(450,803){\makebox(0,0)[r]{0.04}}%
\put(450,551){\makebox(0,0)[r]{0.038}}%
\put(450,300){\makebox(0,0)[r]{0.036}}%
\end{picture}%
\endgroup
\endinput

fig5.tex
% GNUPLOT: LaTeX picture with Postscript
\begingroup%
  \makeatletter%
  \newcommand{\GNUPLOTspecial}{%
    \@sanitize\catcode`\%=14\relax\special}%
  \setlength{\unitlength}{0.1bp}%
{\GNUPLOTspecial{!
%!PS-Adobe-2.0 EPSF-2.0
%%Title: crr_dist_pp.tex
%%Creator: gnuplot 3.7 patchlevel 1
%%CreationDate: Fri Aug 18 12:44:29 2000
%%DocumentFonts:
%%BoundingBox: 0 0 288 216
%%Orientation: Landscape
%%EndComments
/gnudict 256 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/userlinewidth gnulinewidth def
/vshift -33 def
/dl {10 mul} def
/hpt_ 31.5 def
/vpt_ 31.5 def
/hpt hpt_ def
/vpt vpt_ def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def
  /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke userlinewidth 2 mul setlinewidth } def
/AL { stroke userlinewidth 2 div setlinewidth } def
/UL { dup gnulinewidth mul /userlinewidth exch def
      10 mul /udl exch def } def
/PL { stroke userlinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 1 0 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 1 0 DL } def
/LT2 { PL [2 dl 3 dl] 0 0 1 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/Pnt { stroke [] 0 setdash
   gsave 1 setlinecap M 0 0 V stroke grestore } def
/Dia { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  Pnt } def
/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  Pnt } def
/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  Pnt  } def
/Star { 2 copy Pls Crs } def
/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V  hpt2 0 V  0 vpt2 V
  hpt2 neg 0 V  closepath fill } def
/TriUF { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath fill } def
/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke
  Pnt  } def
/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath fill} def
/DiaF { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath fill } def
/Pent { stroke [] 0 setdash 2 copy gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore Pnt } def
/PentF { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath fill grestore } def
/Circle { stroke [] 0 setdash 2 copy
  hpt 0 360 arc stroke Pnt } def
/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def
/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450  arc } bind def
/C1 { BL [] 0 setdash 2 copy        moveto
       2 copy  vpt 0 90 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C2 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C3 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C4 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C5 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 90 arc
       2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc } bind def
/C6 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 90 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C7 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 0 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C8 { BL [] 0 setdash 2 copy moveto
      2 copy vpt 270 360 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C9 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 270 450 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill
       2 copy moveto
       2 copy vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C11 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
       2 copy moveto
       2 copy  vpt 270 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C12 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C13 { BL [] 0 setdash  2 copy moveto
       2 copy  vpt 0 90 arc closepath fill
       2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C14 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 360 arc closepath fill
               vpt 0 360 arc } bind def
/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/Rec   { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
       neg 0 rlineto closepath } bind def
/Square { dup Rec } bind def
/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def
/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def
/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def
/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def
/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill
       exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill
       2 copy vpt Square fill
       Bsquare } bind def
/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def
/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill
       Bsquare } bind def
/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill
       Bsquare } bind def
/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def
/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy vpt Square fill Bsquare } bind def
/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def
/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def
/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def
/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def
/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def
/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def
/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def
/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def
/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def
/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def
/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def
/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def
/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def
/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def
/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def
/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def
/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def
/DiaE { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke } def
/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke } def
/TriUE { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke } def
/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke } def
/PentE { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore } def
/CircE { stroke [] 0 setdash
  hpt 0 360 arc stroke } def
/Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def
/DiaW { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V Opaque stroke } def
/BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V Opaque stroke } def
/TriUW { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V Opaque stroke } def
/TriDW { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V Opaque stroke } def
/PentW { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  Opaque stroke grestore } def
/CircW { stroke [] 0 setdash
  hpt 0 360 arc Opaque stroke } def
/BoxFill { gsave Rec 1 setgray fill grestore } def
end
%%EndProlog
}}%
\begin{picture}(2880,2160)(0,0)%
{\GNUPLOTspecial{"
gnudict begin
gsave
0 0 translate
0.100 0.100 scale
0 setgray
newpath
1.000 UL
LTb
450 503 M
63 0 V
2217 0 R
-63 0 V
450 842 M
63 0 V
2217 0 R
-63 0 V
450 1180 M
63 0 V
2217 0 R
-63 0 V
450 1518 M
63 0 V
2217 0 R
-63 0 V
450 1857 M
63 0 V
2217 0 R
-63 0 V
450 300 M
0 63 V
0 1697 R
0 -63 V
690 300 M
0 63 V
0 1697 R
0 -63 V
930 300 M
0 63 V
0 1697 R
0 -63 V
1170 300 M
0 63 V
0 1697 R
0 -63 V
1410 300 M
0 63 V
0 1697 R
0 -63 V
1650 300 M
0 63 V
0 1697 R
0 -63 V
1890 300 M
0 63 V
0 1697 R
0 -63 V
2130 300 M
0 63 V
0 1697 R
0 -63 V
2370 300 M
0 63 V
0 1697 R
0 -63 V
2610 300 M
0 63 V
0 1697 R
0 -63 V
1.000 UL
LTb
450 300 M
2280 0 V
0 1760 V
-2280 0 V
450 300 L
1.000 UP
1.000 UL
LT0
1450 1947 M
263 0 V
-263 31 R
0 -62 V
263 62 R
0 -62 V
769 1314 M
0 105 V
738 1314 M
62 0 V
-62 105 R
62 0 V
1060 773 M
0 135 V
1029 773 M
62 0 V
-62 135 R
62 0 V
261 -92 R
0 159 V
1321 816 M
62 0 V
-62 159 R
62 0 V
260 -52 R
0 221 V
1612 923 M
62 0 V
-62 221 R
62 0 V
1934 943 M
0 356 V
1903 943 M
62 0 V
-62 356 R
62 0 V
261 -199 R
0 577 V
-31 -577 R
62 0 V
-62 577 R
62 0 V
769 1366 TriU
1060 841 TriU
1352 895 TriU
1643 1034 TriU
1934 1121 TriU
2226 1388 TriU
1581 1947 TriU
1.000 UP
1.000 UL
LT0
1450 1847 M
263 0 V
-263 31 R
0 -62 V
263 62 R
0 -62 V
817 1323 M
0 79 V
-31 -79 R
62 0 V
-62 79 R
62 0 V
1108 777 M
0 89 V
-31 -89 R
62 0 V
-62 89 R
62 0 V
261 -74 R
0 129 V
1369 792 M
62 0 V
-62 129 R
62 0 V
260 43 R
0 162 V
1660 964 M
62 0 V
-62 162 R
62 0 V
260 -94 R
0 226 V
-31 -226 R
62 0 V
-62 226 R
62 0 V
261 -202 R
0 376 V
-31 -376 R
62 0 V
-62 376 R
62 0 V
2565 616 M
0 790 V
2534 616 M
62 0 V
-62 790 R
62 0 V
817 1363 Box
1108 822 Box
1400 856 Box
1691 1045 Box
1982 1145 Box
2274 1244 Box
2565 1011 Box
1581 1847 Box
1.000 UP
1.000 UL
LT0
1450 1747 M
263 0 V
-263 31 R
0 -62 V
263 62 R
0 -62 V
793 1413 M
0 66 V
-31 -66 R
62 0 V
-62 66 R
62 0 V
1084 893 M
0 83 V
-31 -83 R
62 0 V
-62 83 R
62 0 V
261 -59 R
0 106 V
1345 917 M
62 0 V
-62 106 R
62 0 V
260 -9 R
0 145 V
-31 -145 R
62 0 V
-62 145 R
62 0 V
260 5 R
0 267 V
-31 -267 R
62 0 V
-62 267 R
62 0 V
261 -274 R
0 345 V
-31 -345 R
62 0 V
-62 345 R
62 0 V
2541 475 M
0 629 V
2510 475 M
62 0 V
-62 629 R
62 0 V
793 1446 BoxF
1084 934 BoxF
1376 970 BoxF
1667 1086 BoxF
1958 1297 BoxF
2250 1329 BoxF
2541 789 BoxF
1581 1747 BoxF
1.000 UP
1.000 UL
LT0
1450 1647 M
263 0 V
-263 31 R
0 -62 V
263 62 R
0 -62 V
638 1120 M
0 91 V
-31 -91 R
62 0 V
-62 91 R
62 0 V
840 563 M
0 92 V
809 563 M
62 0 V
-62 92 R
62 0 V
1042 434 M
0 132 V
1011 434 M
62 0 V
-62 132 R
62 0 V
171 -87 R
0 157 V
1213 479 M
62 0 V
-62 157 R
62 0 V
171 -52 R
0 219 V
1415 584 M
62 0 V
-62 219 R
62 0 V
171 -19 R
0 292 V
1617 784 M
62 0 V
-62 292 R
62 0 V
1850 874 M
0 346 V
1819 874 M
62 0 V
-62 346 R
62 0 V
171 -103 R
0 457 V
-31 -457 R
62 0 V
-62 457 R
62 0 V
171 -391 R
0 781 V
-31 -781 R
62 0 V
-62 781 R
62 0 V
638 1166 Circle
840 609 Circle
1042 500 Circle
1244 558 Circle
1446 694 Circle
1648 930 Circle
1850 1047 Circle
2052 1345 Circle
2254 1574 Circle
1581 1647 Circle
1.000 UP
1.000 UL
LT0
1450 1547 M
263 0 V
-263 31 R
0 -62 V
263 62 R
0 -62 V
614 1124 M
0 144 V
583 1124 M
62 0 V
-62 144 R
62 0 V
816 537 M
0 153 V
785 537 M
62 0 V
785 690 M
62 0 V
1018 430 M
0 183 V
987 430 M
62 0 V
987 613 M
62 0 V
1220 454 M
0 216 V
1189 454 M
62 0 V
-62 216 R
62 0 V
1422 521 M
0 265 V
1391 521 M
62 0 V
-62 265 R
62 0 V
1624 683 M
0 324 V
1593 683 M
62 0 V
-62 324 R
62 0 V
1826 745 M
0 378 V
1795 745 M
62 0 V
-62 378 R
62 0 V
2028 882 M
0 490 V
1997 882 M
62 0 V
-62 490 R
62 0 V
2230 897 M
0 679 V
2199 897 M
62 0 V
-62 679 R
62 0 V
2432 591 M
0 1118 V
2401 591 M
62 0 V
-62 1118 R
62 0 V
614 1196 CircleF
816 614 CircleF
1018 522 CircleF
1220 562 CircleF
1422 653 CircleF
1624 845 CircleF
1826 934 CircleF
2028 1127 CircleF
2230 1237 CircleF
2432 1150 CircleF
1581 1547 CircleF
stroke
grestore
end
showpage
}}%
\put(1400,1547){\makebox(0,0)[r]{\footnotesize $L=24,~~~~"~"~~~$}}%
\put(1400,1647){\makebox(0,0)[r]{\footnotesize $L=20,~\beta=2.5$}}%
\put(1400,1747){\makebox(0,0)[r]{\footnotesize $L=24,~~~~"~"~~~$}}%
\put(1400,1847){\makebox(0,0)[r]{\footnotesize $L=20,~~~~"~"~~~$}}%
\put(1400,1947){\makebox(0,0)[r]{\footnotesize $L=16,~\beta=2.4$}}%
\put(1590,50){\makebox(0,0){$r=I \cdot a~~(fm) $}}%
\put(100,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$\chi_{Z(2)}(I,I)/\sigma_{SU(2)}a^2$}}%
\special{ps: currentpoint grestore moveto}%
}%
\put(2610,200){\makebox(0,0){1}}%
\put(2370,200){\makebox(0,0){0.9}}%
\put(2130,200){\makebox(0,0){0.8}}%
\put(1890,200){\makebox(0,0){0.7}}%
\put(1650,200){\makebox(0,0){0.6}}%
\put(1410,200){\makebox(0,0){0.5}}%
\put(1170,200){\makebox(0,0){0.4}}%
\put(930,200){\makebox(0,0){0.3}}%
\put(690,200){\makebox(0,0){0.2}}%
\put(450,200){\makebox(0,0){0.1}}%
\put(400,1857){\makebox(0,0)[r]{0.75}}%
\put(400,1518){\makebox(0,0)[r]{0.7}}%
\put(400,1180){\makebox(0,0)[r]{0.65}}%
\put(400,842){\makebox(0,0)[r]{0.6}}%
\put(400,503){\makebox(0,0)[r]{0.55}}%
\end{picture}%
\endgroup
\endinput

fig6.tex
% GNUPLOT: LaTeX picture with Postscript
\begingroup%
  \makeatletter%
  \newcommand{\GNUPLOTspecial}{%
    \@sanitize\catcode`\%=14\relax\special}%
  \setlength{\unitlength}{0.1bp}%
{\GNUPLOTspecial{!
%!PS-Adobe-2.0 EPSF-2.0
%%Title: t-fit2.tex
%%Creator: gnuplot 3.7 patchlevel 1
%%CreationDate: Fri Aug 11 14:37:08 2000
%%DocumentFonts: 
%%BoundingBox: 0 0 288 216
%%Orientation: Landscape
%%EndComments
/gnudict 256 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/userlinewidth gnulinewidth def
/vshift -33 def
/dl {10 mul} def
/hpt_ 31.5 def
/vpt_ 31.5 def
/hpt hpt_ def
/vpt vpt_ def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def
  /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke userlinewidth 2 mul setlinewidth } def
/AL { stroke userlinewidth 2 div setlinewidth } def
/UL { dup gnulinewidth mul /userlinewidth exch def
      10 mul /udl exch def } def
/PL { stroke userlinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 1 0 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 1 0 DL } def
/LT2 { PL [2 dl 3 dl] 0 0 1 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/Pnt { stroke [] 0 setdash
   gsave 1 setlinecap M 0 0 V stroke grestore } def
/Dia { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  Pnt } def
/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  Pnt } def
/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  Pnt  } def
/Star { 2 copy Pls Crs } def
/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V  hpt2 0 V  0 vpt2 V
  hpt2 neg 0 V  closepath fill } def
/TriUF { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath fill } def
/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke
  Pnt  } def
/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath fill} def
/DiaF { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath fill } def
/Pent { stroke [] 0 setdash 2 copy gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore Pnt } def
/PentF { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath fill grestore } def
/Circle { stroke [] 0 setdash 2 copy
  hpt 0 360 arc stroke Pnt } def
/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def
/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450  arc } bind def
/C1 { BL [] 0 setdash 2 copy        moveto
       2 copy  vpt 0 90 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C2 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C3 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C4 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C5 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 90 arc
       2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc } bind def
/C6 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 90 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C7 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 0 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C8 { BL [] 0 setdash 2 copy moveto
      2 copy vpt 270 360 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C9 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 270 450 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill
       2 copy moveto
       2 copy vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C11 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
       2 copy moveto
       2 copy  vpt 270 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C12 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C13 { BL [] 0 setdash  2 copy moveto
       2 copy  vpt 0 90 arc closepath fill
       2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C14 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 360 arc closepath fill
               vpt 0 360 arc } bind def
/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/Rec   { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
       neg 0 rlineto closepath } bind def
/Square { dup Rec } bind def
/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def
/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def
/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def
/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def
/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill
       exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill
       2 copy vpt Square fill
       Bsquare } bind def
/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def
/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill
       Bsquare } bind def
/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill
       Bsquare } bind def
/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def
/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy vpt Square fill Bsquare } bind def
/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def
/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def
/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def
/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def
/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def
/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def
/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def
/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def
/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def
/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def
/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def
/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def
/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def
/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def
/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def
/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def
/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def
/DiaE { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke } def
/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke } def
/TriUE { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke } def
/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke } def
/PentE { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore } def
/CircE { stroke [] 0 setdash 
  hpt 0 360 arc stroke } def
/Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def
/DiaW { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V Opaque stroke } def
/BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V Opaque stroke } def
/TriUW { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V Opaque stroke } def
/TriDW { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V Opaque stroke } def
/PentW { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  Opaque stroke grestore } def
/CircW { stroke [] 0 setdash 
  hpt 0 360 arc Opaque stroke } def
/BoxFill { gsave Rec 1 setgray fill grestore } def
end
%%EndProlog
}}%
\begin{picture}(2880,2160)(0,0)%
{\GNUPLOTspecial{"
gnudict begin
gsave
0 0 translate
0.100 0.100 scale
0 setgray
newpath
1.000 UL
LTb
400 300 M
63 0 V
2267 0 R
-63 0 V
400 520 M
63 0 V
2267 0 R
-63 0 V
400 740 M
63 0 V
2267 0 R
-63 0 V
400 960 M
63 0 V
2267 0 R
-63 0 V
400 1180 M
63 0 V
2267 0 R
-63 0 V
400 1400 M
63 0 V
2267 0 R
-63 0 V
400 1620 M
63 0 V
2267 0 R
-63 0 V
400 1840 M
63 0 V
2267 0 R
-63 0 V
400 2060 M
63 0 V
2267 0 R
-63 0 V
594 300 M
0 63 V
0 1697 R
0 -63 V
983 300 M
0 63 V
0 1697 R
0 -63 V
1371 300 M
0 63 V
0 1697 R
0 -63 V
1759 300 M
0 63 V
0 1697 R
0 -63 V
2148 300 M
0 63 V
0 1697 R
0 -63 V
2536 300 M
0 63 V
0 1697 R
0 -63 V
1.000 UL
LTb
400 300 M
2330 0 V
0 1760 V
-2330 0 V
400 300 L
0.700 UP
1.000 UL
LT0
594 464 M
0 2 V
-31 -2 R
62 0 V
-62 2 R
62 0 V
163 -4 R
0 2 V
-31 -2 R
62 0 V
-62 2 R
62 0 V
164 -2 R
0 2 V
-31 -2 R
62 0 V
-62 2 R
62 0 V
163 -2 R
0 2 V
-31 -2 R
62 0 V
-62 2 R
62 0 V
163 -1 R
0 2 V
-31 -2 R
62 0 V
-62 2 R
62 0 V
163 -2 R
0 2 V
-31 -2 R
62 0 V
-62 2 R
62 0 V
163 -2 R
0 2 V
-31 -2 R
62 0 V
-62 2 R
62 0 V
163 -5 R
0 8 V
-31 -8 R
62 0 V
-62 8 R
62 0 V
164 -10 R
0 12 V
-31 -12 R
62 0 V
-62 12 R
62 0 V
163 -13 R
0 14 V
-31 -14 R
62 0 V
-62 14 R
62 0 V
163 -19 R
0 24 V
-31 -24 R
62 0 V
-62 24 R
62 0 V
594 465 Circle
788 463 Circle
983 463 Circle
1177 463 Circle
1371 464 Circle
1565 464 Circle
1759 464 Circle
1953 464 Circle
2148 464 Circle
2342 464 Circle
2536 464 Circle
0.700 UP
1.000 UL
LT0
594 781 M
0 7 V
-31 -7 R
62 0 V
-62 7 R
62 0 V
788 759 M
0 8 V
-31 -8 R
62 0 V
-62 8 R
62 0 V
164 -7 R
0 9 V
-31 -9 R
62 0 V
-62 9 R
62 0 V
163 -4 R
0 9 V
-31 -9 R
62 0 V
-62 9 R
62 0 V
163 -6 R
0 11 V
-31 -11 R
62 0 V
-62 11 R
62 0 V
163 -9 R
0 10 V
-31 -10 R
62 0 V
-62 10 R
62 0 V
163 -8 R
0 10 V
-31 -10 R
62 0 V
-62 10 R
62 0 V
163 -15 R
0 23 V
-31 -23 R
62 0 V
-62 23 R
62 0 V
164 -30 R
0 44 V
-31 -44 R
62 0 V
-62 44 R
62 0 V
163 -49 R
0 55 V
-31 -55 R
62 0 V
-62 55 R
62 0 V
163 -96 R
0 137 V
2505 714 M
62 0 V
-62 137 R
62 0 V
594 785 Circle
788 763 Circle
983 765 Circle
1177 770 Circle
1371 774 Circle
1565 775 Circle
1759 777 Circle
1953 779 Circle
2148 782 Circle
2342 782 Circle
2536 783 Circle
0.700 UP
1.000 UL
LT0
594 1204 M
0 16 V
-31 -16 R
62 0 V
-62 16 R
62 0 V
163 -63 R
0 19 V
-31 -19 R
62 0 V
-62 19 R
62 0 V
164 -13 R
0 21 V
-31 -21 R
62 0 V
-62 21 R
62 0 V
163 -11 R
0 26 V
-31 -26 R
62 0 V
-62 26 R
62 0 V
163 -18 R
0 31 V
-31 -31 R
62 0 V
-62 31 R
62 0 V
163 -25 R
0 32 V
-31 -32 R
62 0 V
-62 32 R
62 0 V
163 -43 R
0 39 V
-31 -39 R
62 0 V
-62 39 R
62 0 V
163 -93 R
0 201 V
-31 -201 R
62 0 V
-62 201 R
62 0 V
594 1212 Circle
788 1167 Circle
983 1174 Circle
1177 1186 Circle
1371 1197 Circle
1565 1203 Circle
1759 1196 Circle
1953 1222 Circle
0.700 UP
1.000 UL
LT0
594 1631 M
0 26 V
-31 -26 R
62 0 V
-62 26 R
62 0 V
163 -96 R
0 31 V
-31 -31 R
62 0 V
-62 31 R
62 0 V
164 -10 R
0 40 V
-31 -40 R
62 0 V
-62 40 R
62 0 V
163 -29 R
0 55 V
-31 -55 R
62 0 V
-62 55 R
62 0 V
163 -12 R
0 78 V
-31 -78 R
62 0 V
-62 78 R
62 0 V
163 -61 R
0 102 V
-31 -102 R
62 0 V
-62 102 R
62 0 V
163 -243 R
0 226 V
-31 -226 R
62 0 V
-62 226 R
62 0 V
594 1644 Circle
788 1576 Circle
983 1602 Circle
1177 1621 Circle
1371 1675 Circle
1565 1704 Circle
1759 1625 Circle
1.000 UL
LT0
400 468 M
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
1.000 UL
LT0
400 775 M
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
1.000 UL
LT0
400 1199 M
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
1.000 UL
LT0
400 1681 M
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
23 0 V
24 0 V
stroke
grestore
end
showpage
}}%
\put(1410,1835){\makebox(0,0)[l]{$R=12$}}%
\put(1410,578){\makebox(0,0)[l]{$R=1$}}%
\put(1410,885){\makebox(0,0)[l]{$R=4$}}%
\put(1410,1309){\makebox(0,0)[l]{$R=8$}}%
\put(1565,50){\makebox(0,0){$T$}}%
\put(100,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$V_{Z(2)}(R,T)$}}%
\special{ps: currentpoint grestore moveto}%
}%
\put(2536,200){\makebox(0,0){12}}%
\put(2148,200){\makebox(0,0){10}}%
\put(1759,200){\makebox(0,0){8}}%
\put(1371,200){\makebox(0,0){6}}%
\put(983,200){\makebox(0,0){4}}%
\put(594,200){\makebox(0,0){2}}%
\put(350,2060){\makebox(0,0)[r]{0.8}}%
\put(350,1840){\makebox(0,0)[r]{0.7}}%
\put(350,1620){\makebox(0,0)[r]{0.6}}%
\put(350,1400){\makebox(0,0)[r]{0.5}}%
\put(350,1180){\makebox(0,0)[r]{0.4}}%
\put(350,960){\makebox(0,0)[r]{0.3}}%
\put(350,740){\makebox(0,0)[r]{0.2}}%
\put(350,520){\makebox(0,0)[r]{0.1}}%
\put(350,300){\makebox(0,0)[r]{0}}%
\end{picture}%
\endgroup
\endinput

fig7.tex
% GNUPLOT: LaTeX picture with Postscript
\begingroup%
  \makeatletter%
  \newcommand{\GNUPLOTspecial}{%
    \@sanitize\catcode`\%=14\relax\special}%
  \setlength{\unitlength}{0.1bp}%
{\GNUPLOTspecial{!
%!PS-Adobe-2.0 EPSF-2.0
%%Title: pot_24_fin.tex
%%Creator: gnuplot 3.7 patchlevel 1
%%CreationDate: Fri Aug 18 13:47:17 2000
%%DocumentFonts: 
%%BoundingBox: 0 0 288 216
%%Orientation: Landscape
%%EndComments
/gnudict 256 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/userlinewidth gnulinewidth def
/vshift -33 def
/dl {10 mul} def
/hpt_ 31.5 def
/vpt_ 31.5 def
/hpt hpt_ def
/vpt vpt_ def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def
  /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke userlinewidth 2 mul setlinewidth } def
/AL { stroke userlinewidth 2 div setlinewidth } def
/UL { dup gnulinewidth mul /userlinewidth exch def
      10 mul /udl exch def } def
/PL { stroke userlinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 1 0 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 1 0 DL } def
/LT2 { PL [2 dl 3 dl] 0 0 1 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/Pnt { stroke [] 0 setdash
   gsave 1 setlinecap M 0 0 V stroke grestore } def
/Dia { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  Pnt } def
/Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  Pnt } def
/Crs { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  Pnt  } def
/Star { 2 copy Pls Crs } def
/BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V  hpt2 0 V  0 vpt2 V
  hpt2 neg 0 V  closepath fill } def
/TriUF { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath fill } def
/TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke
  Pnt  } def
/TriDF { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath fill} def
/DiaF { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath fill } def
/Pent { stroke [] 0 setdash 2 copy gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore Pnt } def
/PentF { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath fill grestore } def
/Circle { stroke [] 0 setdash 2 copy
  hpt 0 360 arc stroke Pnt } def
/CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def
/C0 { BL [] 0 setdash 2 copy moveto vpt 90 450  arc } bind def
/C1 { BL [] 0 setdash 2 copy        moveto
       2 copy  vpt 0 90 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C2 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C3 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C4 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C5 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 90 arc
       2 copy moveto
       2 copy  vpt 180 270 arc closepath fill
               vpt 0 360 arc } bind def
/C6 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 90 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C7 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 0 270 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C8 { BL [] 0 setdash 2 copy moveto
      2 copy vpt 270 360 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C9 { BL [] 0 setdash 2 copy moveto
      2 copy  vpt 270 450 arc closepath fill
              vpt 0 360 arc closepath } bind def
/C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill
       2 copy moveto
       2 copy vpt 90 180 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C11 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 0 180 arc closepath fill
       2 copy moveto
       2 copy  vpt 270 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C12 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C13 { BL [] 0 setdash  2 copy moveto
       2 copy  vpt 0 90 arc closepath fill
       2 copy moveto
       2 copy  vpt 180 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/C14 { BL [] 0 setdash 2 copy moveto
       2 copy  vpt 90 360 arc closepath fill
               vpt 0 360 arc } bind def
/C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill
               vpt 0 360 arc closepath } bind def
/Rec   { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
       neg 0 rlineto closepath } bind def
/Square { dup Rec } bind def
/Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def
/S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def
/S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def
/S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def
/S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill
       exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def
/S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill
       2 copy vpt Square fill
       Bsquare } bind def
/S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def
/S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def
/S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill
       Bsquare } bind def
/S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill
       Bsquare } bind def
/S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def
/S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy vpt Square fill Bsquare } bind def
/S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
       2 copy exch vpt sub exch vpt Square fill Bsquare } bind def
/S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def
/D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def
/D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def
/D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def
/D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def
/D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def
/D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def
/D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def
/D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def
/D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def
/D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def
/D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def
/D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def
/D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def
/D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def
/D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def
/D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def
/DiaE { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke } def
/BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke } def
/TriUE { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke } def
/TriDE { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V closepath stroke } def
/PentE { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  closepath stroke grestore } def
/CircE { stroke [] 0 setdash 
  hpt 0 360 arc stroke } def
/Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def
/DiaW { stroke [] 0 setdash vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V Opaque stroke } def
/BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V Opaque stroke } def
/TriUW { stroke [] 0 setdash vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V Opaque stroke } def
/TriDW { stroke [] 0 setdash vpt 1.12 mul sub M
  hpt neg vpt 1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt -1.62 mul V Opaque stroke } def
/PentW { stroke [] 0 setdash gsave
  translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
  Opaque stroke grestore } def
/CircW { stroke [] 0 setdash 
  hpt 0 360 arc Opaque stroke } def
/BoxFill { gsave Rec 1 setgray fill grestore } def
end
%%EndProlog
}}%
\begin{picture}(2880,2160)(0,0)%
{\GNUPLOTspecial{"
gnudict begin
gsave
0 0 translate
0.100 0.100 scale
0 setgray
newpath
1.000 UL
LTb
400 300 M
63 0 V
2267 0 R
-63 0 V
400 593 M
63 0 V
2267 0 R
-63 0 V
400 887 M
63 0 V
2267 0 R
-63 0 V
400 1180 M
63 0 V
2267 0 R
-63 0 V
400 1473 M
63 0 V
2267 0 R
-63 0 V
400 1767 M
63 0 V
2267 0 R
-63 0 V
400 2060 M
63 0 V
2267 0 R
-63 0 V
704 300 M
0 63 V
0 1697 R
0 -63 V
1109 300 M
0 63 V
0 1697 R
0 -63 V
1514 300 M
0 63 V
0 1697 R
0 -63 V
1920 300 M
0 63 V
0 1697 R
0 -63 V
2325 300 M
0 63 V
0 1697 R
0 -63 V
2730 300 M
0 63 V
0 1697 R
0 -63 V
1.000 UL
LTb
400 300 M
2330 0 V
0 1760 V
-2330 0 V
400 300 L
0.800 UP
1.000 UL
LT0
501 515 M
0 3 V
-31 -3 R
62 0 V
-62 3 R
62 0 V
704 653 M
0 6 V
-31 -6 R
62 0 V
-62 6 R
62 0 V
907 780 M
0 10 V
876 780 M
62 0 V
-62 10 R
62 0 V
171 121 R
0 13 V
-31 -13 R
62 0 V
-62 13 R
62 0 V
172 112 R
0 18 V
-31 -18 R
62 0 V
-62 18 R
62 0 V
171 114 R
0 30 V
-31 -30 R
62 0 V
-62 30 R
62 0 V
172 96 R
0 36 V
-31 -36 R
62 0 V
-62 36 R
62 0 V
172 76 R
0 47 V
-31 -47 R
62 0 V
-62 47 R
62 0 V
171 91 R
0 58 V
-31 -58 R
62 0 V
-62 58 R
62 0 V
172 85 R
0 71 V
-31 -71 R
62 0 V
-62 71 R
62 0 V
171 64 R
0 94 V
-31 -94 R
62 0 V
-62 94 R
62 0 V
501 516 Circle
704 656 Circle
907 785 Circle
1109 917 Circle
1312 1045 Circle
1514 1183 Circle
1717 1312 Circle
1920 1429 Circle
2122 1573 Circle
2325 1723 Circle
2527 1869 Circle
1.000 UL
LT0
400 436 M
24 21 V
23 19 V
24 18 V
23 17 V
24 17 V
23 17 V
24 16 V
23 16 V
24 16 V
23 16 V
24 15 V
23 16 V
24 16 V
23 15 V
24 16 V
24 15 V
23 16 V
24 15 V
23 15 V
24 16 V
23 15 V
24 15 V
23 16 V
24 15 V
23 15 V
24 15 V
23 16 V
24 15 V
24 15 V
23 15 V
24 16 V
23 15 V
24 15 V
23 15 V
24 16 V
23 15 V
24 15 V
23 15 V
24 15 V
23 16 V
24 15 V
23 15 V
24 15 V
24 15 V
23 15 V
24 16 V
23 15 V
24 15 V
23 15 V
24 15 V
23 15 V
24 16 V
23 15 V
24 15 V
23 15 V
24 15 V
24 15 V
23 16 V
24 15 V
23 15 V
24 15 V
23 15 V
24 15 V
23 16 V
24 15 V
23 15 V
24 15 V
23 15 V
24 15 V
23 15 V
24 16 V
24 15 V
23 15 V
24 15 V
23 15 V
24 15 V
23 15 V
24 16 V
23 15 V
24 15 V
23 15 V
24 15 V
23 15 V
24 15 V
24 16 V
23 15 V
24 15 V
23 15 V
24 15 V
23 15 V
24 15 V
23 16 V
24 15 V
23 15 V
24 15 V
23 15 V
24 15 V
23 15 V
24 15 V
stroke
grestore
end
showpage
}}%
\put(1565,50){\makebox(0,0){$R$}}%
\put(100,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$V_{Z(2)}(R)$}}%
\special{ps: currentpoint grestore moveto}%
}%
\put(2730,200){\makebox(0,0){12}}%
\put(2325,200){\makebox(0,0){10}}%
\put(1920,200){\makebox(0,0){8}}%
\put(1514,200){\makebox(0,0){6}}%
\put(1109,200){\makebox(0,0){4}}%
\put(704,200){\makebox(0,0){2}}%
\put(350,2060){\makebox(0,0)[r]{0.6}}%
\put(350,1767){\makebox(0,0)[r]{0.5}}%
\put(350,1473){\makebox(0,0)[r]{0.4}}%
\put(350,1180){\makebox(0,0)[r]{0.3}}%
\put(350,887){\makebox(0,0)[r]{0.2}}%
\put(350,593){\makebox(0,0)[r]{0.1}}%
\put(350,300){\makebox(0,0)[r]{0}}%
\end{picture}%
\endgroup
\endinput

hep-lat0009035.extracted_bib
\begin{thebibliography}{99}
\newcommand{\npb}[1]{{\it Nucl.~Phys.}~{\bf B#1}\ }
\newcommand{\plb}[1]{{\it Phys.~Lett.}~{\bf #1B}\ }

\bibitem{center_v} G. 't Hooft, \npb{138},1 (1978);\\
J.M. Cornwall, \npb{157},392 (1979); \\
G. Mack, in Recent Developments in Gauge Theories, ed. by G. 't Hooft et al.
(Plenum, New York, 1980); \\
H.B. Nielsen and P. Olesen, \npb{160} (1979) 380; \\
J. Ambjorn and P. Olesen, \npb{170} (1980) 60; 265.

\bibitem{tomb1}  T.G. Kovacs and E. T. Tomboulis,
{\it J.Math.Phys.} {\bf 40} (1999) 4677.

\bibitem{greens1} L. Del Debbio, M. Faber, J. Greensite and S. Olejnik,
{\it Phys.Rev.} {\bf D55} (1997) 2298.

\bibitem{greens2} L. Del Debbio, M. Faber, J. Giedt, J. Greensite and S.
Olejnik, {\it Phys.Rev.} {\bf D58} (1998) 094501.

\bibitem{def}
Ph. de Forcrand and M. D'Elia, {\it Phys.Rev.Lett.} {\bf 82} (1999) 4582; \\
C. Alexandrou, M. D'Elia and Ph. de Forcrand,~ {\it Nucl.Phys.} {\bf B}
[Proc.Suppl.] {\bf 83}(2000)~437.

\bibitem{bvz} B.L.~Bakker, A.I.~Veselov and M.A.~Zubkov,
hep-lat/007022.

\bibitem{gribov} V.N.~Gribov, \npb{139} (1978) 1.

\bibitem{tomb2}  T.G. Kovacs and E.T. Tomboulis,
{\it Phys.Lett.} {\bf B463} (1999) 104.

\bibitem{bkpv1} V.G. Bornyakov, D.A. Komarov, M.I. Polikarpov
and A.I. Veselov, {\it JETP Lett.} {\bf 71} (2000) 231.

\bibitem{bkpv2} V.G. Bornyakov, D.A. Komarov, M.I. Polikarpov
and A.I. Veselov, To be published in Proceedings of the
International Symposium on Quantum Chromodynamics and Color
Confinement (Confinement 2000), Osaka, Japan, 7-10 Mar 2000.

\bibitem{greens_osaka} J. Greensite, hep-lat/0005001.

\bibitem{bfgo} R. Bertle, M. Faber, J. Greensite, S. Olejnik,
 hep-lat/0007043.

\bibitem{tubing} K. Langfeld, O. Tennert, M. Engelhardt and H. Reinhardt,
{\it Phys.Lett.} {\bf B452} (1999) 301.

\bibitem{mandula} J.E.~ Mandula and M.C.~ Ogilvie, \plb{185} (1987)~127.

\bibitem{nakajima} H.~Nakajima, S.~Furui and A.~Yamaguchi,~
hep-lat/0007001.

\bibitem{bmmp} A.~Nakamura and M.~Plewnia, \plb{255} (1991)~274; \\
V.~Bornyakov, V.K.~Mitrjushkin, M.~M\"uller-Preussker
 and F.~Pahl, \plb{B317} (1993)~596.

\bibitem{bbms} G.S. Bali, V. Bornyakov, M. M\"uller-Preussker and K.
Schilling, {\it Phys.Rev.} {\bf D54} (1996) 2863.

\bibitem{stochastic} F. Shoji, T. Suzuki, H. Kodama and A. Nakamura,
\plb{476} (2000) 199.

\bibitem{kerler} G. Damm, W. Kerler, \plb{397} (1997) 216.

\bibitem{parfac} S.~Fachin and C.~Parrinello,
{\it Nucl. Phys.} {\bf B} [Proc.~Suppl.] {\bf 26}(1992)~429.

\bibitem{vds} J.C. Vink, U.-J. Wiese,
{\it Phys.Lett.} {\bf B289} (1992) 122; \\
A.J. van der Sijs, {\it Prog.Theor.Phys.Suppl.} {\bf 131} (1998) 149.

\bibitem{saa} S.~Kirkpatrick, C.D.~Gelatt Jr., M.P.~Vecchi,
{\it Science} {\bf 220} (1983) 671; V.~Cerny,
{\it J.\ Opt.\ The.\ Appl.\ } {\bf 45}
(1985) 41.

\bibitem{phm} S. Perantonis, A. Huntley and C. Michael,
\npb{326} (1989) 544.

\bibitem{bss} G.S. Bali, K. Schilling and C. Schlichter,
{\it Phys.Rev.} {\bf D51} (1995) 5165.

\bibitem{gubali} F.V. Gubarev, E.M. Ilgenfritz, M.I. Polikarpov and
T.~Suzuki, {\it Phys. Lett.} {\bf B468} (1999) 134.

\bibitem{jg_priv} J. Greensite, private communication.

\bibitem{defp} Ph. de Forcrand and M. Pepe, hep-lat/0008016.

\end{thebibliography}