Geodesic
Countably Periodic Gibbs Measures of the Ising Model on the Cayley Tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 1, pp. 109-118

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We describe a wide class of normal divisors of infinite index of the group representation of the Cayley tree and study the structure of partitions of the Cayley tree w.r.t. any normal divisor of infinite index. We prove that for a specific normal divisor of infinite index, there are three periodic and uncountably many nonperiodic Gibbs measures for an inhomogeneous Ising model. 
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     author = {U. A. Rozikov},
     title = {Countably {Periodic} {Gibbs} {Measures} of the {Ising} {Model} on the {Cayley} {Tree}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {130},
     number = {1},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_130_1_a6/}
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U. A. Rozikov. Countably Periodic Gibbs Measures of the Ising Model on the Cayley Tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 1, pp. 109-118. http://geodesic.mathdoc.fr/item/TMF_2002_130_1_a6/