This article is cited in 5 papers

On weakly periodic Gibbs measures of the Potts model with a special external field on a Cayley tree

M. M. Rahmatullaev

Institut of Mathematics, 29 Durmon Yuli Str., 100125, Uzbekistan

Abstract: In the paper, we study the $q$-state (where $q=3,4,5,\dots$) Potts model with special external field on a Cayley tree of order $k\geq 2$. For antiferromagnetic Potts model with such an external field on the Cayley tree of order $k\geq 6$, the non-uniqueness of weakly periodic (non-periodic) Gibbs measures is proved. The weakly periodic Gibbs measures for the Potts model with zero external field are also studied. It is proved that under some conditions imposed on the parameters of the model there can be not less than $2^q-2$ such measures.

Key words and phrases: Cayley tree, Gibbs measure, Potts model, weakly periodic measure.

MSC: Primary 82B26; Secondary 60K35

Received: 05.03.2015
Revised: 27.01.2016

Language: English

DOI: 10.15407/mag12.04.302      

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