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Description of periodic extreme gibbs measures of some lattice models on the Cayley tree

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Abstract

The uniqueness of the translation-invariant extreme Gibbs measure for the antiferromagnetic Potts model with an external field and the existence of an uncountable number of extreme Gibbs measures for the Ising model with an external field on the Cayley tree are proved. The classes of normal subgroups of finite index of the Cayley tree group representation are constructed. The periodic extreme Gibbs measures, which are invariant with respect to subgroups of index 2, are constructed for the Ising model with zero external field. From these measures, the existence of an uncountable number of nonperiodic extreme Gibbs measures for the antiferromagnatic Ising model follows.

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Authors and Affiliations

  1. Mathematical Institute, Academy of Sciences of Uzbekistan, USSR

    N. N. Ganikhodzhaev & U. A. Rozikov

Authors
  1. N. N. Ganikhodzhaev
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  2. U. A. Rozikov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 1, pp. 109–117, April, 1997.

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Ganikhodzhaev, N.N., Rozikov, U.A. Description of periodic extreme gibbs measures of some lattice models on the Cayley tree. Theor Math Phys 111, 480–486 (1997). https://doi.org/10.1007/BF02634202

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  • DOI: https://doi.org/10.1007/BF02634202

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