This article is cited in 13 papers

Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree

U. A. Rozikov^a, R. M. Khakimov^b, F. Kh. Khaidarov<sup>c

a</sup> Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
^b Namangam State University, Namangan, Uzbekistan
^c Mirzo Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan

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 $k=3$.

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

Received: 17.08.2017
Revised: 11.10.2017

DOI: 10.4213/tmf9448

 English version: Theoretical and Mathematical Physics, 2018, 196:1, 1043–1058

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