Geodesic
$p$-Adic Gibbs measures for the hard core model with three states on the Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 1, pp. 68-82 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study $p$-adic hard core models with three states on the Cayley tree. It is known that there are four types of such models. We find conditions that must be imposed on the order $k$ of the Cayley tree and on the prime $p$ for a translation-invariant $p$-adic Gibbs measure to exist.
Keywords: Cayley tree, Gibbs measure, hard core $G$-model, translation-invariant measure, $p$-adic number.
Mots-clés : configuration 
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     title = {$p${-Adic} {Gibbs} measures for the~hard core model with three states on {the~Cayley} tree},
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}
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O. N. Khakimov. $p$-Adic Gibbs measures for the hard core model with three states on the Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 1, pp. 68-82. http://geodesic.mathdoc.fr/item/TMF_2013_177_1_a1/

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

[2] U. A. Rozikov, Sh. A. Shoyusupov, TMF, 156:3 (2008), 412–424 | DOI | DOI | MR | Zbl

[3] D. Gandolfo, U. A. Rozikov, J. Ruiz, Markov Process. Related Fields, 18:4 (2012), 701–720 | MR | Zbl

[4] P. M. Bleher, J. Ruiz, V. A. Zagrebnov, J. Statist. Phys., 79:1–2 (1995), 473–482 | DOI | MR | Zbl

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

[6] H.-O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter Studies in Mathematics, 9, Walter de Gruyter, Berlin, 1988 | MR | Zbl

[7] Y. M. Suhov, U. A. Rozikov, Queueing Syst., 46:1–2 (2004), 197–212 | DOI | MR | Zbl

[8] A. Yu. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Mathematics and its Applications, 427, Kluwer, Dordrecht, 1997 | MR | Zbl

[9] E. Marinari, G. Parisi, Phys. Lett. B, 203:1–2 (1988), 52–54 | DOI | MR

[10] B. C. Vladimirov, I. V. Volovich, E. I. Zelenov, $p$-Adicheskii analiz i matematicheskaya fizika, Nauka, M., 1994 | MR

[11] A. C. M. van Rooij, Non-Archimedean Functional Analysis, Monographs and Textbooks in Pure and Applied Mathematics, 51, M. Dekker, New York, 1978 | MR | Zbl

[12] S. Albeverio, W. Karwowski, Stoch. Proc. Appl., 53:1 (1994), 1–22 | DOI | MR | Zbl

[13] S. Albeverio, X. Zhao, Ann. Probab., 28:4 (2000), 1680–1710 | DOI | MR | Zbl

[14] K. Yasuda, Osaka J. Math., 37:4 (2000), 967–985 | MR | Zbl

[15] U. A. Rozikov, O. N. Khakimov, TMF, 175:1 (2013), 84–92 | DOI | DOI | MR | Zbl

[16] N. N. Ganikhodzhaev, F. M. Mukhammedov, U. A. Rozikov, Uzb. matem. zhurn., 4 (1998), 23–29

[17] G. R. Brightwell, P. Winkler, J. Combin. Theory Ser. B, 77:2 (1999), 221–262 | DOI | MR | Zbl

[18] F. F. Turaev, Uzb. matem. zhurn., 2 (2013), 21–29

[19] N. Koblits, $p$-Adicheskie chisla, $p$-adicheskii analiz i dzeta-funktsii, Mir, M., 1982 | MR

[20] W. H. Schikhof, Ultrametric Calculus. An introduction to $p$-adic analysis, Cambridge Studies in Advanced Mathematics, 4, Cambridge Univ. Press, Cambridge, 1984 | MR | Zbl

[21] F. M. Mukhamedov, U. A. Rozikov, Indag. Math. (N. S.), 15:4 (2004), 85–99 | DOI | MR | Zbl