Geodesic
The~existence of weakly periodic Gibbs measures for the~Potts model on
Teoretičeskaâ i matematičeskaâ fizika, Tome 180 (2014) no. 3, pp. 307-317

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We study the $q$-state Potts model on a Cayley tree of order $k\ge2$. In the group representation of the Cayley tree for the ferromagnetic Potts model, we single out a set of index-$2$ subgroups under which each weakly periodic Gibbs measure is translation invariant. For the anti-ferromagnetic Potts model with $k\ge2$ and $q\ge 2$, we show that a weakly periodic Gibbs measure that is not translation invariant is not unique.
Keywords: Cayley tree, Gibbs measure, Potts model, weakly periodic Gibbs measure. 
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     author = {M. M. Rakhmatullaev},
     title = {The~existence of weakly periodic {Gibbs} measures for {the~Potts} model on},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {307--317},
     publisher = {mathdoc},
     volume = {180},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a1/}
}
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M. M. Rakhmatullaev. The~existence of weakly periodic Gibbs measures for the~Potts model on. Teoretičeskaâ i matematičeskaâ fizika, Tome 180 (2014) no. 3, pp. 307-317. http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a1/