Geodesic
Description of weakly periodic Gibbs measures for the Ising model on a Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 2, pp. 292-302 Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce the concept of a weakly periodic Gibbs measure. For the Ising model, we describe a set of such measures corresponding to normal subgroups of indices two and four in the group representation of a Cayley tree. In particular, we prove that for a Cayley tree of order four, there exist critical values $T_{\mathrm{c}} of the temperature $T>0$ such that there exist five weakly periodic Gibbs measures for $0 or $T>T_{\mathrm{cr}}$, three weakly periodic Gibbs measures for $T=T_{\mathrm{c}}$, and one weakly periodic Gibbs measure for $T_{\mathrm{c}}.
Keywords: Cayley tree, Gibbs measure, Ising model, weakly periodic measure. 
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     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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U. A. Rozikov; M. M. Rakhmatullaev. Description of weakly periodic Gibbs measures for the Ising model on a Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 2, pp. 292-302. http://geodesic.mathdoc.fr/item/TMF_2008_156_2_a10/

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