This article is cited in 25 papers

Periodic Gibbs measures for the Potts model on the Cayley tree

U. A. Rozikov^a, R. M. Khakimov<sup>b

a</sup> Institute of Mathematics, Tashkent, Uzbekistan
^b Namangan State University, Namangan, Uzbekistan

Abstract: We study the Potts model on the Cayley tree. We demonstrate that for this model with a zero external field, periodic Gibbs measures on some invariant sets are translation invariant. Furthermore, we find the conditions under which the Potts model with a nonzero external field admits periodic Gibbs measures.

Keywords: Cayley tree, configuration, Potts model, Gibbs measure, periodic measure, translation-invariant measure.

Received: 08.10.2012
Revised: 26.12.2012

DOI: 10.4213/tmf8423

 English version: Theoretical and Mathematical Physics, 2013, 175:2, 699–709

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