Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Translation-invariant and periodic Gibbs measures for Potts model on a
  Cayley tree   In this paper is studied ferromagnetic three states Potts model on a Cayley
tree of order three and we give explicit formulas for translation-invariant
Gibbs measures. Furthermore, we show that under some conditions on the
parameter of the antiferromagnetic Potts model with q-states with zero external
field on the Cayley tree of order $k>2$, there are exactly 2(2^q-1) periodic
(non translation-invariant) Gibbs measures.

16
The categories of this paper are: stat
19
The categories of this paper are: eess
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin