New periodic Gibbs measures for Potts model with q-states on a Cayley tree

TL;DR

This paper proves the existence and characterizes the number of periodic Gibbs measures for the q-state Potts model on a Cayley tree, expanding understanding of phase structures in such models.

Contribution

It introduces new conditions under which periodic Gibbs measures exist for the Potts model on Cayley trees and provides a theorem on their quantity.

Findings

Existence of periodic Gibbs measures under specific parameter conditions

Number of such measures characterized by a new theorem

Non translation-invariant measures identified

Abstract

In this paper under some conditions on parameters of the Potts model with q-states on a Cayley tree of order k it is proved existence of the periodic (non translation-invariant)Gibbs measures. Also given a theorem about the number of these measures.