On periodic Gibbs measures for Potts-SOS model on the Cayley tree

TL;DR

This paper characterizes periodic Gibbs measures for the Potts-SOS model on Cayley trees, providing a detailed description of these measures relative to subgroups of the tree's symmetry group.

Contribution

It offers a new characterization of periodic Gibbs measures for the Potts-SOS model on Cayley trees based on subgroup structures.

Findings

Describes periodic Gibbs measures for the model

Provides a classification based on subgroup analysis

Enhances understanding of phase structures in the model

Abstract

In this paper we give a description of periodic Gibbs measures for Potts-SOS model on the Cayley tree of order $k\geq 1$ , i.e. a characterization of such measures with respect to any normal subgroup of finite index of the group representation of a Cayley tree.