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Partition structures of the cayley tree and applications for describing periodic gibbs distributions

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Abstract

In the group representation of the Cayley tree, the distribution of elements of the partition into conjugate classes of finite-index, normal subgroups is described. For the inhomogeneous Ising model, it is proved that there exist only three H0-periodic Gibbs distributions, where H0 is a normal subgroup of finite index.

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Authors and Affiliations

  1. Institute for Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan Republic

    U. A. Rozikov

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  1. U. A. Rozikov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 112, No. 1, pp. 170–175.

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Rozikov, U.A. Partition structures of the cayley tree and applications for describing periodic gibbs distributions. Theor Math Phys 112, 929–933 (1997). https://doi.org/10.1007/BF02634109

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  • DOI: https://doi.org/10.1007/BF02634109

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