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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 201, Number 1, Pages 126–136
DOI: https://doi.org/10.4213/tmf9711 (Mi tmf9711) 		 
This article is cited in 8 scientific papers (total in 8 papers)

A $p$-adic generalized Gibbs measure for the Ising model on a Cayley tree

M. M. Rahmatullaevab, O. N. Khakimovb, A. M. Tukhtaboevc

a Namangam State University, Namangan, Uzbekistan
b Institute of Mathematics, National University of Uzbekistan named by after Mirzo Ulugbek, Tashkent, Uzbekistan
c Namangan Construction Institute, Namangan, Uzbekistan
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DOI: https://doi.org/10.4213/tmf9711
Abstract: We consider a $p$-adic Ising model on the Cayley tree of order $k\ge2$. We completely describe all $p$-adic translation-invariant generalized Gibbs measures for $k=3$. Moreover, we show the existence of a phase transition for the $p$-adic Ising model for any $k\ge3$ if $p\equiv1\!\pmod4$.
Keywords: $p$-adic number, Ising model, Gibbs measure, phase transition.
Received: 25.02.2019
Revised: 01.04.2019
English version:
Theoretical and Mathematical Physics, 2019, Volume 201, Issue 1, Pages 1521–1530
DOI: https://doi.org/10.1134/S004057791910009X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. M. Rahmatullaev, O. N. Khakimov, A. M. Tukhtaboev, “A $p$-adic generalized Gibbs measure for the Ising model on a Cayley tree”, TMF, 201:1 (2019), 126–136; Theoret. and Math. Phys., 201:1 (2019), 1521–1530
Citation in format AMSBIB
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\paper A~$p$-adic generalized Gibbs measure for the~ Ising model on a~Cayley tree
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\pages 126--136
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  • https://www.mathnet.ru/eng/tmf/v201/i1/p126
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:42
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