A Contour Method on Cayley tree

Abstract

We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define 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.

12 pages

References in corpus (5)

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Cited by in corpus (11)

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• On $p$-adic Gibbs Measures for Hard Core Model on a Cayley Tree
• Extremal inhomogeneous Gibbs states for SOS-models and finite-spin models on trees
• Gibbs measures of Potts model on Cayley trees: a survey and applications
• Percolation on infinite graphs and isoperimetric inequalities
• Cross-over between diffusion-limited and reaction-limited regimes in the coagulation-diffusion process
• Ground states and Gibbs measures of Ising model with competing interactions and an external field on a Cayley tree
• Counting Contours on Trees
• On Ground States of Rozikov Model on the Cayley Tree
• Exact solution of a generalized ANNNI model on a Cayley tree