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 translationinvariant 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.