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

M. M. Rahmatullaev; M. A. Rasulova

doi:10.1088/1742-5468/ac08ff

paper

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

arXiv:2104.00973 · doi:10.1088/1742-5468/ac08ff

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.