Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the absence of zero-temperature limit of equilibrium states for
  finite-range interactions on the lattice $\mathbb{Z}^2$   We construct finite-range interactions on $\mathcal{S}^{\mathbb{Z}^2}$, where
$\mathcal{S}$ is a finite set, for which the associated equilibrium states
(i.e., the shift-invariant Gibbs states) fail to converge as temperature goes
to zero. More precisely, if we pick any one-parameter family
$(\mu_\beta)_{\beta>0}$ in which $\mu_\beta$ is an equilibrium state at inverse
temperature $ \beta$ for this interaction, then
$\lim_{\beta\to\infty}\mu_\beta$ does not exist. This settles a question posed
by the first author and Hochman who obtained such a non-convergence behavior
when $d\geq 3$, $d$ being the dimension of the lattice.

16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph