Extremality of the Translation-Invariant Gibbs Measures for the Potts Model on the Cayley Tree

U. A. Rozikov; R. M. Khakimov; F. Kh. Khaidarov

doi:10.1134/S0040577918070103

Extremality of the Translation-Invariant Gibbs Measures for the Potts Model on the Cayley Tree

Authors: Rozikov U.A.¹, Khakimov R.M.², Khaidarov F.K.³
Affiliations:
1. Romanovskii Institute of Mathematics
2. Namangan State University
3. Mirzo Ulugbek National University of Uzbekistan
Issue: Vol 196, No 1 (2018)
Pages: 1043-1058
Section: Article
URL: https://journals.rcsi.science/0040-5779/article/view/171852
DOI: https://doi.org/10.1134/S0040577918070103
ID: 171852

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Abstract

We study translation-invariant Gibbs measures for the ferromagnetic Potts model with q states on the Cayley tree of order k and generalize some earlier results. We consider the question of the extremality of the known translation-invariant Gibbs measures for the Potts model with three states on the Cayley tree of order k = 3.