Mathematical Physics
[Submitted on 6 Apr 2015 (v1), last revised 22 Mar 2017 (this version, v2)]
Title:Boundary conditions for translation-invariant Gibbs measures of the Potts model on Cayley trees
View PDFAbstract: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 $\mu$.
Submission history
From: Utkir A. Rozikov [view email][v1] Mon, 6 Apr 2015 11:30:45 UTC (789 KB)
[v2] Wed, 22 Mar 2017 05:32:06 UTC (378 KB)
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