GIBBS MEASURES FOR THE ASYMMETRIC CLOCK MODEL ON A CAYLEY TREE

GIBBS MEASURES FOR THE ASYMMETRIC CLOCK MODEL ON A CAYLEY TREE

M. M. Rahmatullaev, B. U. Abraev

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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.

Keywords

Cayley tree, asymmetric clock model, Gibbs measures, phase transitions.