Non uniqueness of $p$-adic Gibbs distribution for the Ising model on the lattice $Z^d$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 1, pp. 123-127.

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In this paper, we show non uniqueness of $p$-adic Gibbs distribution for the Ising model on the $Z^d$. Moreover, we prove that a $p$-adic Gibbs distribution is bounded if and only if $p\neq2$.
Keywords: Gibbs distribution, Ising model, lattice.
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Zohid T. Tugyonov. Non uniqueness of $p$-adic Gibbs distribution for the Ising model on the lattice $Z^d$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 1, pp. 123-127. http://geodesic.mathdoc.fr/item/JSFU_2016_9_1_a13/

[1] U. A. Rozikov, O. N. Khakimov, “$p$-adic Gibbs measures and Markov random fields on countable graphs”, TMPh, 175:1 (2013), 518–525 | MR | Zbl

[2] U. A. Rozikov, Gibbs measures on Cayley trees, World Sci., Publ. Singapore, 2013 | MR | Zbl

[3] V. S. Vladimirov, I. V. Volovich, E. V. Zelenov, $p$-adic Analysis and Mathematical Physics, World Sci., Singapore, 1994 | MR | Zbl

[4] N. Koblitz, $p$-adic numbers, $p$-adic analysis, and zeta-functions, New York, 1984 | MR

[5] A. Yu. Khrennikov, Non-archimedean analysis and its applications, Fizmatlit, M., 2003 (in Russian) | MR | Zbl

[6] H.-O. Georgii, Gibbs Measures and Phase Transitions, W. de Gruyter, Berlin, 1988 | MR | Zbl