Geodesic
Four competing interactions for models with an uncountable set of
Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 3, pp. 503-517

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We consider models with four competing interactions (external field, nearest neighbor, second neighbor, and three neighbors) and an uncountable set $[0,1]$ of spin values on the Cayley tree of order two. We reduce the problem of describing the splitting Gibbs measures of the model to the problem of analyzing solutions of a nonlinear integral equation and study some particular cases for Ising and Potts models. We also show that periodic Gibbs measures for the given models either are translation invariant or have the period two. We present examples where periodic Gibbs measures with the period two are not unique.
Keywords: Cayley tree, competing interaction, Gibbs measure, Ising model, Potts model, periodic Gibbs measure
Mots-clés : configuration, phase transition. 
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     author = {U. A. Rozikov and F. Kh. Khaidarov},
     title = {Four competing interactions for models with an uncountable set of},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {503--517},
     publisher = {mathdoc},
     volume = {191},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_191_3_a8/}
}
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U. A. Rozikov; F. Kh. Khaidarov. Four competing interactions for models with an uncountable set of. Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 3, pp. 503-517. http://geodesic.mathdoc.fr/item/TMF_2017_191_3_a8/