Geodesic
Potts model with competing interactions on the~Cayley tree: The~contour method
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 86-97

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We consider the Potts model with three spin values and with competing interactions of radius $r=2$ on the Cayley tree of order $k=2$. We completely describe the ground states of this model and use the contour method on the tree to prove that this model has three Gibbs measures at sufficiently low temperatures.
Keywords: Cayley tree, ground state, Gibbs measure.
Mots-clés : configuration, contour method 
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     author = {G. I. Botirov and U. A. Rozikov},
     title = {Potts model with competing interactions on {the~Cayley} tree: {The~contour} method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {86--97},
     publisher = {mathdoc},
     volume = {153},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a6/}
}
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G. I. Botirov; U. A. Rozikov. Potts model with competing interactions on the~Cayley tree: The~contour method. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 86-97. http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a6/