Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase separation for the long range one--dimensional ising model   We consider the phase separation problem for the one--dimensional
ferromagnetic Ising model with long--range two--body interaction,
$J(n)=n^{-2+\a}$ where $n\in \N$ denotes the distance of the two spins and $
\alpha \in ]0,\a_+[$ with $\a_+=(\log 3)/(\log 2) -1$. We prove that given
$m\in ]-1,+1[$, if the temperature is small enough, then typical configuration
for the $\mu^{+}$ Gibbs measure conditionally to have a empirical magnetization
of the order $m$ are made of a single interval that occupy almost a proportion
$\frac{1}{2}(1-\frac{m}{m_\b})$ of the volume with the minus phase inside and
the rest of the volume is the plus phase, here $m_\b>0 $ is the spontaneous
magnetization.

37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph