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arXiv · 1504.01265

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

D. Gandolfo·M. M. Rahmatullaev·U. A. Rozikov
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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 $\mu$.

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D. Gandolfo, M. M. Rahmatullaev, U. A. Rozikov. 2015-04-06. Boundary conditions for translation-invariant Gibbs measures of the Potts model on Cayley trees. https://arxiv.org/abs/1504.01265

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