This article is cited in 7 papers

$p$-Adic solid-on-solid model on a Cayley tree

O. N. Khakimov

Institute of Mathematics, Tashkent, Uzbekistan

Abstract: We consider a $p$-adic solid-on-solid (SOS) model with a nearest-neighbor coupling, $m{+}1$ spins, and a coupling constant $J\in\mathbb Q_p$ on a Cayley tree. We find conditions under which a phase transition does not occur in the model. We show that if $p\mid m+1$ for some $J$, then a phase transition occurs. Moreover, we formulate a criterion for the boundedness of $p$-adic Gibbs measures for the $(m+1)$-state SOS model.

Keywords: $p$-adic number, $p$-adic SOS model, Cayley tree, $p$-adic Gibbs measure.

Received: 06.11.2016

DOI: 10.4213/tmf9293

 English version: Theoretical and Mathematical Physics, 2017, 193:3, 1880–1893

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