This article is cited in 13 papers

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

M. M. Rahmatullaev^ab, O. N. Khakimov^b, A. M. Tukhtaboev<sup>c

a</sup> 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.

Received: 25.02.2019
Revised: 01.04.2019

DOI: 10.4213/tmf9711

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

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