Geodesic
Discription of periodic extreme Gibbs measures of some lattice models on the Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 111 (1997) no. 1, pp. 109-117 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that the translational invariant extreme Gibbs measure is unique for the antiferromagnetic Potts model with the external field. The existence of uncountable numbers of the extreme Gibbs measures for the Ising model with the external field on the Cayley tree is proved. The classes of normal subgroups of finite index of group representation of the Cayley tree is constructed. The periodic extreme Gibbs measures invariant with respect to subgroups of index two for the Ising model are constructed and the existence of uncountable numberes of the nonperiodic extreme Gibbs measures for the antiferromagnetic Ising model is proved. 
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N. N. Ganikhodzhaev; U. A. Rozikov. Discription of periodic extreme Gibbs measures of some lattice models on the Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 111 (1997) no. 1, pp. 109-117. http://geodesic.mathdoc.fr/item/TMF_1997_111_1_a7/

[1] R. Bekster, Tochno reshaemye modeli v statisticheskoi mekhanike, Mir, M., 1985 | MR

[2] P. M. Blekher, N. N. Ganikhodzhaev, Teoriya veroyatn. i ee primen., 35:2 (1990), 920–930 | MR

[3] N. N. Ganikhodzhaev, DAN RUz., 1992, no. 6–7, 4–7

[4] N. N. Ganikhodzhaev, TMF, 85:2 (1990), 163–175 | MR

[5] K. Preston, Gibbsovskie sostoyaniya na schetnykh mnozhestvakh, Mir, M., 1977 | MR

[6] P. M. Bleher, Commun. Math. Phys., 128 (1990), 411–419 | DOI | MR | Zbl

[7] H. O. Georgii, Gibbs measures and phase trasitions, De Gru. studies in math., de Gru., Berlin–New York, 1988 | MR | Zbl

[8] F. Spitzer, Ann. Prob., 3 (1975), 387–398 | DOI | MR | Zbl

[9] Y. Higuchi, Publ. RIMS Kyoto Univ., 3 (1977), 335–348 | DOI | MR

[10] N. N. Ganikhodzhaev, DAN RUz., 1994, no. 5, 3–6 | MR

[11] A. G. Kurosh, Teoriya grupp, Nauka, M., 1967 | MR | Zbl

[12] M. I. Kargapolov, Yu. I. Merzlyakov, Osnovy teorii grupp, Nauka, M., 1982 | MR | Zbl

[13] S. A. Pirogov, Ya. G. Sinai, TMF, 25:3 (1975), 358–369 ; 26:1 (1976), 61–76 | MR | MR

[14] Ya. G. Sinai, Teoriya fazovykh perekhodov, Nauka, M., 1980 | MR