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Potts model with competing interactions on the Cayley tree: The contour method

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Abstract

We consider the Potts model with three spin values and with competing interactions of radius r = 2 on the Cayley tree of order k = 2. We completely describe the ground states of this model and use the contour method on the tree to prove that this model has three Gibbs measures at sufficiently low temperatures.

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Authors and Affiliations

  1. Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan

    G. I. Botirov

  2. Romanovskii Mathematical Institute, Tashkent, Uzbekistan

    U. A. Rozikov

Authors
  1. G. I. Botirov
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  2. U. A. Rozikov
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Correspondence to G. I. Botirov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 1, pp. 86–97, October, 2007.

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Botirov, G.I., Rozikov, U.A. Potts model with competing interactions on the Cayley tree: The contour method. Theor Math Phys 153, 1423–1433 (2007). https://doi.org/10.1007/s11232-007-0125-x

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  • DOI: https://doi.org/10.1007/s11232-007-0125-x

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