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New Phase Transitions of the Ising Model on Cayley Trees

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Abstract

We show that the nearest neighbor Ising model on the Cayley tree exhibits new temperature–driven phase transitions. These transitions occur at various inverse temperatures different from the critical one. They are characterised by a change in the number of Gibbs states as well as by a drastic change of the behavior of free energies at these new transition points.

We also consider the model in the presence of an external field and compute the free energies of translation invariant and some alternating boundary conditions.

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Acknowledgements

The authors thank S. Shlosman for interesting discussions.

U.A. Rozikov acknowledges the Université du Sud Toulon Var for financial support and the Centre de Physique Théorique–Marseille for kind hospitality.

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Authors and Affiliations

  1. Aix Marseille Université, CNRS, CPT, UMR 7332, 13288, Marseille, France

    D. Gandolfo & J. Ruiz

  2. Université de Toulon, CNRS, CPT, UMR 7332, 83957, La Garde, France

    D. Gandolfo & J. Ruiz

  3. National University of Uzbekistan, Tashkent, Uzbekistan

    F. H. Haydarov

  4. Institute of Mathematics, 29, Do’rmon Yo’li str., 100125, Tashkent, Uzbekistan

    U. A. Rozikov

Authors
  1. D. Gandolfo
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  2. F. H. Haydarov
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  3. U. A. Rozikov
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  4. J. Ruiz
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Corresponding author

Correspondence to J. Ruiz.

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Gandolfo, D., Haydarov, F.H., Rozikov, U.A. et al. New Phase Transitions of the Ising Model on Cayley Trees. J Stat Phys 153, 400–411 (2013). https://doi.org/10.1007/s10955-013-0836-3

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  • DOI: https://doi.org/10.1007/s10955-013-0836-3

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