Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On phase transitions of the Potts model with three competing
  interactions on Cayley tree   In the present paper we study a phase transition problem for the Potts model
with three competing interactions, the nearest neighbors, the second neighbors
and triples of neighbors and non-zero external field on Cayley tree of order
two. We prove that for some parameter values of the model there is phase
transition. We reduce the problem of describing by limiting Gibbs measures to
the problem of solving a system of nonlinear functional equations. We extend
the results obtained by Ganikhodjaev and Rozikov [Math. Phys. Anal. Geom.,
2009, 12, No. 2, 141-156] on phase transition for the Ising model to the Potts
model setting.

22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat