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Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree

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Abstract

We study translation-invariant Gibbs measures on a Cayley tree of order k = 3 for the ferromagnetic three-state Potts model. We obtain explicit formulas for translation-invariant Gibbs measures. We also consider periodic Gibbs measures on a Cayley tree of order k for the antiferromagnetic q-state Potts model. Moreover, we improve previously obtained results: we find the exact number of periodic Gibbs measures with the period two on a Cayley tree of order k ≥ 3 that are defined on some invariant sets.

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Authors and Affiliations

  1. Institute of Mathematics, Mirzo Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan

    R. M. Khakimov

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

    F. Kh. Khaydarov

Authors
  1. R. M. Khakimov
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  2. F. Kh. Khaydarov
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Correspondence to R. M. Khakimov.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 189, No. 2, pp. 286–295, November, 2016.

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Khakimov, R.M., Khaydarov, F.K. Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree. Theor Math Phys 189, 1651–1659 (2016). https://doi.org/10.1134/S004057791611009X

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  • DOI: https://doi.org/10.1134/S004057791611009X

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