Boundary conditions for translation-invariant Gibbs measures of the Potts model on Cayley trees

2015/04/06 by Daniel Gandolfo, Gandolfo, D., M. M. Rahmatullaev +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1504.01265

openalex publication_date 2015/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider translation-invariant splitting Gibbs measures (TISGMs) for the q-state Potts model on a Cayley tree of order two. Recently a full description of the TISGMs was obtained, and it was shown in particular that at sufficiently low temperatures their number is 2^q-1. In this paper for each TISGM μ we explicitly give the set of boundary conditions such that limiting Gibbs measures with respect to these boundary conditions coincide with μ.

Citations

• Fuzzy transformations and extremality of Gibbs measures for the Potts model on a Cayley tree

Related

• Description of all translation-invariant p-adic Gibbs measures for the Potts model on a Cayley tree
• Fuzzy transformations and extremality of Gibbs measures for the Potts model on a Cayley tree
• On p-state p-adic Potts model on a Cayley tree
• On three-state Potts model on a Cayley tree: periodic measures
• Gibbs measure for mixed spins and mixed types model