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TMF, 2019, Volume 201, Number 1, Pages 126–136 (Mi tmf9711)  

$p$-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

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.

DOI: https://doi.org/10.4213/tmf9711

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English version:
Theoretical and Mathematical Physics, 2019, 201:1, 1521–1530

Bibliographic databases:

Received: 25.02.2019
Revised: 01.04.2019

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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\by M.~M.~Rahmatullaev, O.~N.~Khakimov, A.~M.~Tukhtaboev
\paper A~$p$-adic generalized Gibbs measure for the~ Ising model on a~Cayley tree
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\yr 2019
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\issue 1
\pages 126--136
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\yr 2019
\vol 201
\issue 1
\pages 1521--1530
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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