Geodesic
Localization of translation-invariant Gibbs measures for the Potts and “solid-on-solid” models on a Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 1, pp. 24-35 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study Potts and “solid-on-solid” models with $q\ge2$ states on the Cayley tree of order $k\ge1$. For any values of the parameter $q$ in the Potts model and $q\le6$ in the “solid-on-solid” model, we find sets containing all translation-invariant Gibbs measures.
Keywords: Cayley tree, Gibbs measure, Potts model, “solid-on-solid” model, periodic measure, translation-invariant measure.
Mots-clés : configuration 
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     author = {R. M. Khakimov},
     title = {Localization of translation-invariant {Gibbs} measures for {the~Potts} and {\textquotedblleft}solid-on-solid{\textquotedblright} models on {a~Cayley} tree},
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R. M. Khakimov. Localization of translation-invariant Gibbs measures for the Potts and “solid-on-solid” models on a Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 1, pp. 24-35. http://geodesic.mathdoc.fr/item/TMF_2014_179_1_a2/

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

[2] C. J. Preston, Gibbs States on Countable Sets, Cambridge Tracts in Mathematics, 68, Cambridge Univ. Press, Cambridge, 1974 | MR | Zbl

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

[4] U. A. Rozikov, Gibbs Measures on Cayley Trees, World Sci., Singapore, 2013 | MR | Zbl

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

[6] N. N. Ganikhodzhaev, DAN RUz, 6–7 (1992), 4–7

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

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

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

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

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

[12] F. Wagner, D. Grensing, J. Heide, J. Phys. A, 34:50 (2001), 11261–11272 | DOI | MR | Zbl

[13] A. E. Mazel, Yu. M. Suhov, J. Statist. Phys., 64:1–2 (1991), 111–134 | DOI | MR | Zbl

[14] U. A. Rozikov, Yu. M. Suhov, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 9:3 (2006), 471–488 | DOI | MR | Zbl

[15] U. A. Rozikov, R. M. Khakimov, TMF, 175:2 (2013), 300–312 | DOI | DOI | MR | Zbl