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Non-uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree

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Abstract

In this paper we construct several models with nearest-neighbor interactions and with the set [0,1] of spin values, on a Cayley tree of order k≥2. We prove that each of the constructed model has at least two translational-invariant Gibbs measures.

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Acknowledgements

U. Rozikov thanks Institut des Hautes Études Scientifiques (IHES), Bures-sur-Yvette, France for support of his visit to IHES and IMU/CDC-program for a (travel) support. We thank referees for their useful suggestions.

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Authors and Affiliations

  1. National University of Uzbekistan, Tashkent, Uzbekistan

    Y. K. Eshkabilov & F. H. Haydarov

  2. Institute of Mathematics, Tashkent, Uzbekistan

    U. A. Rozikov

Authors
  1. Y. K. Eshkabilov
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  2. F. H. Haydarov
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  3. U. A. Rozikov
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Correspondence to U. A. Rozikov.

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Eshkabilov, Y.K., Haydarov, F.H. & Rozikov, U.A. Non-uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree. J Stat Phys 147, 779–794 (2012). https://doi.org/10.1007/s10955-012-0494-x

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  • DOI: https://doi.org/10.1007/s10955-012-0494-x

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