Geodesic
Translation-invariant and periodic Gibbs measures for the~Potts model on a~Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 2, pp. 286-295

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We study translation-invariant Gibbs measures on a Cayley tree of order $k=3$ for the ferromagnetic three-state Potts model. We obtain explicit formulas for translation-invariant Gibbs measures. We also consider periodic Gibbs measures on a Cayley tree of order $k$ for the antiferromagnetic $q$-state Potts model. Moreover, we improve previously obtained results: we find the exact number of periodic Gibbs measures with the period two on a Cayley tree of order $k\ge3$ that are defined on some invariant sets.
Keywords: Cayley tree, Potts model, Gibbs measure, translation-invariant measure, periodic measure.
Mots-clés : configuration 
@article{TMF_2016_189_2_a8,
     author = {R. M. Khakimov and F. Kh. Khaidarov},
     title = {Translation-invariant and periodic {Gibbs} measures for {the~Potts} model on {a~Cayley} tree},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {286--295},
     publisher = {mathdoc},
     volume = {189},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_189_2_a8/}
}
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R. M. Khakimov; F. Kh. Khaidarov. Translation-invariant and periodic Gibbs measures for the~Potts model on a~Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 2, pp. 286-295. http://geodesic.mathdoc.fr/item/TMF_2016_189_2_a8/