This article is cited in 9 papers

Periodic Gibbs Measures for the Ising Model with Competing Interactions

Kh. A. Nazarov^a, U. A. Rozikov<sup>b

a</sup> Samarkand State Institute of Architecture and Construction
^b Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: For the Ising model with competing interactions on the second-order Cayley tree, we find the operator corresponding to the periodic Gibbs distributions with period two and determine the invariant subsets of this operator, which are used to describe the periodic Gibbs distributions.

Keywords: Cayley tree, configuration, limit Gibbs measure, periodic Gibbs measure.

Received: 22.05.2002

DOI: 10.4213/tmf201

 English version: Theoretical and Mathematical Physics, 2003, 135:3, 881–888

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