Gibbs measures for the asymmetric clock model on a Cayley tree

Abstract

We consider the p-state clock model on the Cayley tree and derive a system of functional equations governing this model. Each positive solution of the system corresponds to a splitting Gibbs measure. Utilizing this framework, we investigate the translation-invariant splitting Gibbs measures (TISGMs) of the four-state clock model on the Cayley tree of order two.