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


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Article Info

DATE

1997-04

AUTHORS

N. N. Ganikhodzhaev, U. A. Rozikov

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. More... »

PAGES

480-486

References to SciGraph publications

  • 1975-12. Phase diagrams of classical lattice systems in THEORETICAL AND MATHEMATICAL PHYSICS
  • 1990-03. Extremity of the disordered phase in the Ising model on the Bethe lattice in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1990-11. Pure phases of the ferromagnetic Potts model with three states on a second-order Bethe lattice in THEORETICAL AND MATHEMATICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1007/bf02634202

    DOI

    http://dx.doi.org/10.1007/bf02634202

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1042152983


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