Geodesic
Periodic Gibbs measures for the Potts model on the Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 2, pp. 300-312 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the Potts model on the Cayley tree. We demonstrate that for this model with a zero external field, periodic Gibbs measures on some invariant sets are translation invariant. Furthermore, we find the conditions under which the Potts model with a nonzero external field admits periodic Gibbs measures.
Keywords: Cayley tree, Potts model, Gibbs measure, periodic measure, translation-invariant measure.
Mots-clés : configuration 
@article{TMF_2013_175_2_a9,
     author = {U. A. Rozikov and R. M. Khakimov},
     title = {Periodic {Gibbs} measures for {the~Potts} model on {the~Cayley} tree},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {300--312},
     year = {2013},
     volume = {175},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_175_2_a9/}
}
TY  - JOUR
AU  - U. A. Rozikov
AU  - R. M. Khakimov
TI  - Periodic Gibbs measures for the Potts model on the Cayley tree
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2013
SP  - 300
EP  - 312
VL  - 175
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2013_175_2_a9/
LA  - ru
ID  - TMF_2013_175_2_a9
ER  - 
%0 Journal Article
%A U. A. Rozikov
%A R. M. Khakimov
%T Periodic Gibbs measures for the Potts model on the Cayley tree
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2013
%P 300-312
%V 175
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2013_175_2_a9/
%G ru
%F TMF_2013_175_2_a9
U. A. Rozikov; R. M. Khakimov. Periodic Gibbs measures for the Potts model on the Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 2, pp. 300-312. http://geodesic.mathdoc.fr/item/TMF_2013_175_2_a9/

[1] Kh.-O. Georgi, Gibbsovskie mery i fazovye perekhody, Mir, M., 1992 | MR | Zbl

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

[3] Ya. G. Sinai, Teoriya fazovykh perekhodov. Strogie rezultaty, Nauka, M., 1980 | MR | MR | Zbl

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

[5] N. N. Ganikhodzhaev, Dokl. AN RUz, 6–7 (1992), 4–7

[6] N. N. Ganikhodzhaev, U. A. Rozikov, TMF, 111:1 (1997), 109–117 | DOI | MR | Zbl

[7] N. N. Ganikhodjaev, U. A. Rozikov, Lett. Math. Phys., 75:2 (2006), 99–109 | DOI | MR | Zbl

[8] F. S. de Aguiar, F. A. Bosco, A. S. Martinez, S. Goulart Rosa Jr., J. Stat. Phys., 58:5–6 (1990), 1231–1238 | DOI | MR

[9] F. S. de Aguiar, L. B. Bernardes, S. Goulart Rosa Jr., J. Stat. Phys., 64:3–4 (1991), 673–682 | DOI | MR | Zbl

[10] A. V. Bakaev, A. N. Ermilov, A. M. Kurbatov, Dokl. AN SSSR, 299:3 (1988), 603–606 | MR

[11] F. Peruggi, F. di Liberto, G. Monroy, Phys. A, 131:1 (1985), 300–310 | DOI | MR

[12] F. Peruggi, J. Math. Phys., 25:11 (1984), 3303–3315 | DOI | MR

[13] F. Peruggi, F. di Liberto, G. Monroy, J. Phys. A, 16:4 (1983), 811–827 | DOI | MR

[14] F. Wagner, D. Grensing, J. Heide, J. Phys. A, 34:50 (2001), 11261–11272, arXiv: cond-mat/0110286 | DOI | MR | Zbl

[15] J. B. Martin, U. A. Rozikov, Yu. M. Suhov, J. Nonlin. Math. Phys., 12:3 (2005), 432–448 | DOI | MR | Zbl