Geodesic
Gibbs measures for a~generalized Potts model with the~interaction radius two on a~Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 3, pp. 450-459

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We study a generalized Potts model on a Cayley tree of order $k=3$. Under some conditions on the parameters, we show that there exist at most two translation-invariant Gibbs measures and a continuum of Gibbs measures that are not translation invariant. For any index-two normal divisor $\widehat G$ of the group realizing the Cayley tree, we study $\widehat hG$-periodic Gibbs measures. The existence of an uncountable set of $\widehat hG$-periodic Gibbs measures (which are not translation invariant and not “checkerboard” periodic) is proved.
Keywords: Cayley tree, generalized Potts model, Gibbs measure.
Mots-clés : configuration 
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     author = {N. M. Khatamov and G. T. Madgoziev},
     title = {Gibbs measures for a~generalized {Potts} model with the~interaction radius two on {a~Cayley} tree},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2015_183_3_a7/}
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N. M. Khatamov; G. T. Madgoziev. Gibbs measures for a~generalized Potts model with the~interaction radius two on a~Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 3, pp. 450-459. http://geodesic.mathdoc.fr/item/TMF_2015_183_3_a7/