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Extremality of the Translation-Invariant Gibbs Measures for the Potts Model on the Cayley Tree

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Abstract

We study translation-invariant Gibbs measures for the ferromagnetic Potts model with q states on the Cayley tree of order k and generalize some earlier results. We consider the question of the extremality of the known translation-invariant Gibbs measures for the Potts model with three states on the Cayley tree of order k = 3.

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Authors and Affiliations

  1. Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

    U. A. Rozikov

  2. Namangan State University, Namangan, Uzbekistan

    R. M. Khakimov

  3. Mirzo Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan

    F. Kh. Khaidarov

Authors
  1. U. A. Rozikov
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  2. R. M. Khakimov
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  3. F. Kh. Khaidarov
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Corresponding author

Correspondence to U. A. Rozikov.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 196, No. 1, pp. 117–134, July, 2018.

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Rozikov, U.A., Khakimov, R.M. & Khaidarov, F.K. Extremality of the Translation-Invariant Gibbs Measures for the Potts Model on the Cayley Tree. Theor Math Phys 196, 1043–1058 (2018). https://doi.org/10.1134/S0040577918070103

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  • DOI: https://doi.org/10.1134/S0040577918070103

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