Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigorous Analysis of Singularities and Absence of Analytic Continuation
  at First Order Phase Transition Points in Lattice Spin Models   We report about two new rigorous results on the non-analytic properties of
thermodynamic potentials at first order phase transition. The first one is
valid for lattice models ($d\geq 2$) with arbitrary finite state space, and
finite-range interactions which have two ground states. Under the only
assumption that the Peierls Condition is satisfied for the ground states and
that the temperature is sufficiently low, we prove that the pressure has no
analytic continuation at the first order phase transition point. The second
result concerns Ising spins with Kac potentials
$J_\gamma(x)=\gamma^d\phi(\gamma x)$, where $0<\gamma<1$ is a small scaling
parameter, and $\phi$ a fixed finite range potential. In this framework, we
relate the non-analytic behaviour of the pressure at the transition point to
the range of interaction, which equals $\gamma^{-1}$. Our analysis exhibits a
crossover between the non-analytic behaviour of finite range models
($\gamma>0$) and analyticity in the mean field limit ($\gamma\searrow 0$). In
general, the basic mechanism responsible for the appearance of a singularity
blocking the analytic continuation is that arbitrarily large droplets of the
other phase become stable at the transition point.

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The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
1
The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin