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Periodic Gibbs measures for the Potts model on the Cayley tree

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Abstract

We study the Potts model on the Cayley tree. We demonstrate that for this model with a zero external field, periodic Gibbs measures on some invariant sets are translation invariant. Furthermore, we find the conditions under which the Potts model with a nonzero external field admits periodic Gibbs measures.

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Authors and Affiliations

  1. Institute of Mathematics, Tashkent, Uzbekistan

    U. A. Rozikov

  2. Namangan State University, Namangan, Uzbekistan

    R. M. Khakimov

Authors
  1. U. A. Rozikov
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  2. R. M. Khakimov
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Correspondence to U. A. Rozikov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 175, No. 2, pp. 300–312, May 2013.

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Rozikov, U.A., Khakimov, R.M. Periodic Gibbs measures for the Potts model on the Cayley tree. Theor Math Phys 175, 699–709 (2013). https://doi.org/10.1007/s11232-013-0055-8

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  • DOI: https://doi.org/10.1007/s11232-013-0055-8

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