Description of All Translation-Invariant $\boldsymbol{p}$-Adic Gibbs Measures for the Potts Model on a Cayley Tree

#### O.N. Khakimov, U.A. Rozikov

2015, v.21, Issue 1, 177-204

ABSTRACT

Recently it was proved that usual (real) Potts model on a Cayley tree has up
to $2^q-1$ translation-invariant Gibbs measures. This paper is devoted to description of translation-
invariant $p$-adic Gibbs measures (TIpGMs) of the $p$-adic Potts model. In particular, for the Cayley tree
of order two we give exact number of such measures. Mereover we give
criterion of boundedness of TIpGMs.

Keywords: $p$-adic number, $p$-adic Potts model, Cayley tree, $p$-adic Gibbs measure