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On Weakly Periodic Gibbs Measures for the Potts Model with External Field on the Cayley Tree

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Ukrainian Mathematical Journal Aims and scope

We study the Potts model with external field on a Cayley tree of order k ≥ 2. For the antiferromagnetic Potts model with external field and k ≥ 6 and q ≥ 3, it is shown that the weakly periodic Gibbs measure, which is not periodic, is not unique. For the Potts model with external field equal to zero, we also study weakly periodic Gibbs measures. It is shown that, under certain conditions, the number of these measures cannot be smaller than 2q − 2.

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Authors and Affiliations

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

    M. M. Rakhmatullaev

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  1. M. M. Rakhmatullaev
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 4, pp. 529–541, April, 2016.

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Rakhmatullaev, M.M. On Weakly Periodic Gibbs Measures for the Potts Model with External Field on the Cayley Tree. Ukr Math J 68, 598–611 (2016). https://doi.org/10.1007/s11253-016-1244-z

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  • DOI: https://doi.org/10.1007/s11253-016-1244-z

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