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

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 $\mu$ we explicitly give the set of boundary conditions such that limiting Gibbs measures with respect to these boundary conditions coincide with $\mu$.

15 pages, 8 figures

References in corpus (2)

• Description of the translation-invariant splitting 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

Cited by in corpus (1)

• Phase transitions for Quantum Markov Chains associated with Ising type models on a Cayley tree