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

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 (GMs) for this model in some conditions. Moreover, we investigate whether these GMs are extremal or non-extremal in the set of all GMs.