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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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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DOI: https://doi.org/10.1007/s10955-007-9455-1