Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ordinary, extraordinary, and normal surface transitions:
  extraordinary-normal equivalence and simple explanation of
  $|T-T_c|^{2-\alpha}$ singularities   With simple, exact arguments we show that the surface magnetization $m_1$ at
the extraordinary and normal transitions and the surface energy density
$\epsilon_1$ at the ordinary, extraordinary, and normal transitions of
semi-infinite $d$-dimensional Ising systems have leading thermal singularities
$B_\pm |t|^{2-\alpha}$, with the same critical exponent and amplitude ratio as
the bulk free energy $f_b(t,0)$. The derivation is carried out in three steps:
(i) By tracing out the surface spins, the semi-infinite Ising model with
supercritical surface enhancement $g$ and vanishing surface magnetic field
$h_1$ is mapped exactly onto a semi-infinite Ising model with subcritical
surface enhancement, a nonzero surface field, and irrelevant additional surface
interactions. This establishes the equivalence of the extraordinary ($h_1=0,
g>0$) and normal ($h_1\neq 0, g<0$) transitions. (ii) The magnetization $m_1$
at the interface of an infinite system with uniform temperature $t$ and a
nonzero magnetic field $h$ in the half-space $z>0$ only is shown to be
proportional to $f_b(t,0)-f_b(t,h)$. (iii) The energy density $\epsilon_1$ at
the interface of an infinite system with temperatures $t_+$ and $t$ in the
half-spaces $z>0$ and $z<0$ and no magnetic field is shown to be proportional
to $f_b(t,0)-f_b(t_+,0)$.

22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat