This article is cited in 4 papers

Countably Periodic Gibbs Measures of the Ising Model on the Cayley Tree

U. A. Rozikov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We describe a wide class of normal divisors of infinite index of the group representation of the Cayley tree and study the structure of partitions of the Cayley tree w.r.t. any normal divisor of infinite index. We prove that for a specific normal divisor of infinite index, there are three periodic and uncountably many nonperiodic Gibbs measures for an inhomogeneous Ising model.

Received: 30.01.2001
Revised: 30.04.2001

DOI: 10.4213/tmf293

 English version: Theoretical and Mathematical Physics, 2002, 130:1, 92–100

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