Extremality of translation-invariant Gibbs measures for the Potts-SOS model on the Cayley tree

TL;DR

This paper characterizes all translation-invariant Gibbs measures for the Potts-SOS model on a Cayley tree and examines their extremality, contributing to understanding phase transitions in this statistical physics model.

Contribution

It provides a complete description of translation-invariant Gibbs measures for the Potts-SOS model on a Cayley tree and analyzes their extremality properties.

Findings

All translation-invariant splitting Gibbs measures are described under certain conditions.

The extremality or non-extremality of these measures is determined.

Results contribute to understanding phase transitions in the model.

Abstract

In this paper, we consider the Potts-SOS model where the spin takes values in the set $\{0, 1, 2\}$ on the Cayley tree of order two. We describe all the translation-invariant splitting Gibbs measures for this model in some conditions. Moreover, we investigate whether these Gibbs measures are extremal or non-extremal in the set of all Gibbs measures.