This article is cited in 10 papers

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

R. M. Khakimov^a, F. Kh. Khaidarov<sup>b

a</sup> Institute of Mathematics, National University of Uzbekistan named by after Mirzo Ulugbek, Tashkent, Uzbekistan
^b Mirzo Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: We study translation-invariant Gibbs measures on a Cayley tree of order $k=3$ for the ferromagnetic three-state Potts model. We obtain explicit formulas for translation-invariant Gibbs measures. We also consider periodic Gibbs measures on a Cayley tree of order $k$ for the antiferromagnetic $q$-state Potts model. Moreover, we improve previously obtained results: we find the exact number of periodic Gibbs measures with the period two on a Cayley tree of order $k\ge3$ that are defined on some invariant sets.

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

Received: 22.12.2015

DOI: 10.4213/tmf9138

 English version: Theoretical and Mathematical Physics, 2016, 189:2, 1651–1659

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