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

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 extern...

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Bibliographic Details
Published in:arXiv.org 2016-02
Main Authors: Khakimov, R M, Haydarov, F H
Format: Article
Language:English
Subjects:
Antiferromagnetism
Ferromagnetism
Invariants
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1602.06840