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

D. Gandolfo, M. M. Rakhmatullaev, U. A. Rozikov

Published 2015-04-06Version 1

We consider translation-invariant splitting Gibbs measures (TISGMs) for the $q$-state Potts model on a Cayley tree. 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 $\mu$.