On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field

@article{Bogachev2019OnTU,
title={On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field},
author={Leonid V. Bogachev and Utkir A. Rozikov},
journal={Journal of Statistical Mechanics: Theory and Experiment},
year={2019}
}
• Published 27 March 2019
• Mathematics, Physics
• Journal of Statistical Mechanics: Theory and Experiment
The paper concerns the $q$-state Potts model (i.e., with spin values in $\{1,\dots,q\}$) on a Cayley tree $\mathbb{T}^k$ of degree $k\geq 2$ (i.e., with $k+1$ edges emanating from each vertex) in an external (possibly random) field. We construct the so-called splitting Gibbs measures (SGM) using generalized boundary conditions on a sequence of expanding balls, subject to a suitable compatibility criterion. Hence, the problem of existence/uniqueness of SGM is reduced to solvability of the…

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