Translation-invariant Gibbs measures for Potts model with competing interactions with a countable set of spin values on Cayley tree

Authors

Zarinabonu Mustafoyeva, V.I.Romanovskii Institute of Mathematics, Tashkent, UzbekistanFollow

Abstract

In the present paper we consider of an infinite system of functional equations for the Potts model with competing interactions and countable spin values Φ = {0, 1, ..., } on a Cayley tree of order k. We study translation-invariant Gibbs measures that gives the description of the solutions of some infinite system of equations. For any k ≥ 1 and any fixed probability measure ν we show that the set of translation-invariant splitting Gibbs measures contains one and two points for odd k and even k, respectively, independently on parameters of the Potts model with a countable set of spin values on a Cayley tree.

First Page

202

Last Page

213

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Recommended Citation

Mustafoyeva, Zarinabonu (2023) "Translation-invariant Gibbs measures for Potts model with competing interactions with a countable set of spin values on Cayley tree," Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 6: Iss. 4, Article 4.
DOI: https://doi.org/10.56017/2181-1318.1261