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A Contour Method on Cayley Trees

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Abstract

We consider finite-range lattice models on Cayley trees with two basic properties: the existence of only a finite number of ground states and with a Peierls type condition. We define the notion of a contour for the model on the Cayley tree. By a contour argument we show the existence of s different (where s is the number of ground states) Gibbs measures.

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Authors and Affiliations

  1. Institute of Mathematics and Information Technologies, 29, F. Hodjaev str., 100125, Tashkent, Uzbekistan

    U. A. Rozikov

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  1. U. A. Rozikov
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Correspondence to U. A. Rozikov.

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Dedicated to N.N. Ganikhodjaev on the occasion of his 60th birthday.

The work supported by NATO Reintegration Grant: FEL.RIG.980771.

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Rozikov, U.A. A Contour Method on Cayley Trees. J Stat Phys 130, 801–813 (2008). https://doi.org/10.1007/s10955-007-9455-1

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