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.
@article{JSFU_2016_9_1_a13,
author = {Zohid T. Tugyonov},
title = {Non uniqueness of $p$-adic {Gibbs} distribution for the {Ising} model on the lattice $Z^d$},
journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
pages = {123--127},
year = {2016},
volume = {9},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JSFU_2016_9_1_a13/}
}
TY - JOUR AU - Zohid T. Tugyonov TI - Non uniqueness of $p$-adic Gibbs distribution for the Ising model on the lattice $Z^d$ JO - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika PY - 2016 SP - 123 EP - 127 VL - 9 IS - 1 UR - http://geodesic.mathdoc.fr/item/JSFU_2016_9_1_a13/ LA - en ID - JSFU_2016_9_1_a13 ER -
%0 Journal Article %A Zohid T. Tugyonov %T Non uniqueness of $p$-adic Gibbs distribution for the Ising model on the lattice $Z^d$ %J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika %D 2016 %P 123-127 %V 9 %N 1 %U http://geodesic.mathdoc.fr/item/JSFU_2016_9_1_a13/ %G en %F JSFU_2016_9_1_a13
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