This article is cited in 117 papers

Discription of periodic extreme Gibbs measures of some lattice models on the Cayley tree

N. N. Ganikhodzhaev, U. A. Rozikov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: It is proved that the translational invariant extreme Gibbs measure is unique for the antiferromagnetic Potts model with the external field. The existence of uncountable numbers of the extreme Gibbs measures for the Ising model with the external field on the Cayley tree is proved. The classes of normal subgroups of finite index of group representation of the Cayley tree is constructed. The periodic extreme Gibbs measures invariant with respect to subgroups of index two for the Ising model are constructed and the existence of uncountable numberes of the nonperiodic extreme Gibbs measures for the antiferromagnetic Ising model is proved.

Received: 16.04.1996

DOI: 10.4213/tmf993

 English version: Theoretical and Mathematical Physics, 1997, 111:1, 480–486

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