On three-state Potts model on a Cayley tree: periodic measures

TL;DR

This paper investigates the three-state Potts model on a Cayley tree, demonstrating the existence of exactly two non-translation-invariant periodic Gibbs measures under certain parameter conditions.

Contribution

It establishes the precise number of periodic Gibbs measures for the three-state Potts model on Cayley trees, extending understanding of phase structures in such models.

Findings

Exactly two periodic Gibbs measures exist under certain conditions.

The measures are non-translation-invariant.

Results apply to Cayley trees of order greater than 2.

Abstract

In this paper we show that under some conditions on the parameter of the Potts model with three states with zero external field on the Cayley tree of order $k>2$, there are exactly two periodic (non translation-invariant) Gibbs measures.