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On the Constructive Description of Gibbs Measures for the Potts Model on a Cayley Tree

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Ukrainian Mathematical Journal Aims and scope

We consider the Potts model on a Cayley tree and prove the existence of Gibbs measures constructed by the method proposed in [H. Akin, U. A. Rozikov, and S. Temir, J. Stat. Phys., 142, 314 (2011)]. In addition, we prove that there exist (k0)-translation invariant Gibbs measures for the Potts model on a Cayley tree and compute the free energy of these Gibbs measures.

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Authors and Affiliations

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

    M. M. Rahmatullaev

  2. Kokand State Pedagogic University, Kokand, Uzbekistan

    F. K. Rafikov & Sh. Kh. Azamov

Authors
  1. M. M. Rahmatullaev
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  2. F. K. Rafikov
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  3. Sh. Kh. Azamov
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Corresponding author

Correspondence to M. M. Rahmatullaev.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 7, pp. 938–950, July, 2021. Ukrainian DOI: 10.37863/umzh.v73i7.6408.

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Rahmatullaev, M.M., Rafikov, F.K. & Azamov, S.K. On the Constructive Description of Gibbs Measures for the Potts Model on a Cayley Tree. Ukr Math J 73, 1092–1106 (2021). https://doi.org/10.1007/s11253-021-01979-y

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  • DOI: https://doi.org/10.1007/s11253-021-01979-y

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