Geodesic
Partition structures of the Cayley tree and applications for describing periodic Gibbs distributions
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 1, pp. 170-175

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The disposition order of partition elements into adjacent classes of the group representation of the Cayley tree on its finite index normal subgroups is described. For the inhomogeneous Ising model it is proved that there exist three $H_0$-periodic Gibbs distributions, where $H_0$ is a normal subgroup of finite index. 
@article{TMF_1997_112_1_a12,
     author = {U. A. Rozikov},
     title = {Partition structures of the {Cayley} tree and applications for describing periodic {Gibbs} distributions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {170--175},
     publisher = {mathdoc},
     volume = {112},
     number = {1},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_112_1_a12/}
}
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U. A. Rozikov. Partition structures of the Cayley tree and applications for describing periodic Gibbs distributions. Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 1, pp. 170-175. http://geodesic.mathdoc.fr/item/TMF_1997_112_1_a12/