Translation-invariant and periodic Gibbs measures for Potts model on a Cayley tree

Abstract

In this paper is studied ferromagnetic three states Potts model on a Cayley tree of order three and we give explicit formulas for translation-invariant Gibbs measures. Furthermore, we show that under some conditions on the parameter of the antiferromagnetic Potts model with q-states with zero external field on the Cayley tree of order $k>2$, there are exactly 2(2^q-1) periodic (non translation-invariant) Gibbs measures.

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Cited by in corpus (2)

• Gibbs measures of Potts model on Cayley trees: a survey and applications
• Translation-invariance of periodic Gibbs measures for the Potts model on the Cayley tree