This article is cited in 1 paper

Anisotropic Ising model with countable set of spin values on Cayley tree

Golibjon I. Botirov

Institute of mathematics, Do’rmon Yo’li, 29, Tashkent, 100125, Uzbekistan

Abstract: In this paper we investigate of an infinite system of functional equations for the Ising model with competing interactions and countable spin values $0,1,\ldots$ and non zero filed on a Cayley tree of order two. We derived an infinite system of functional equations for the Ising model that is we describe conditions on $h_x$ guaranteeing compatibility of distributions $\mu^{(n)}(\sigma_n)$.

Keywords: Cayley tree, Ising model, Gibbs measures, functional equations, compatibility of distributions measures.

UDC: 517.98

Received: 26.04.2016
Received in revised form: 04.07.2016
Accepted: 10.02.2017

Language: English

DOI: 10.17516/1997-1397-2017-10-3-305-309

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