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NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2016, 7 (3), P. 401–404

Functional equations for the Potts model with competing interactions on a Cayley tree

G. I. Botirov – Institute of Mathematics, National University of Uzbekistan; botirovg@yandex.ru

In this paper, we consider an infinite system of functional equations for the Potts model with competing interactions of radius r = 2 and countable spin values 0, 1, . . . . . , and non-zero-filled, on a Cayley tree of order two. We describe conditions on h_x guaranteeing compatibility of distributions μ⁽ⁿ⁾(σ_(n)).

Keywords: Cayley tree, Potts model, Gibbs measures, functional equations.

PACS 05.50.+q, 05.70.Fh, 02.30.-f, 02.50.Ga

DOI 10.17586/2220-8054-2016-7-3-401-404

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