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.

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