This article is cited in 37 papers

$\mathbb {Z}$Existence of a Phase Transition for the Potts $p$-adic Model on the Set $\mathbb {Z}$

N. N. Ganikhodzhaev, F. M. Mukhamedov, U. A. Rozikov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We consider the Potts model on the set $\mathbb {Z}$ in the field $Q_p$ of $p$-adic numbers. The range of the spin variables $\sigma (n)$, $n\in \mathbb Z$, in this model is $\Phi =\{\sigma _1,\sigma _2,\dots \dots ,\sigma _q\}\subset Q_p^{q-1}=\underbrace {Q_p\times Q_p\times \dots \times Q_p}_{q-1}$. We show that there are some values $q=q(p)$ for which phase transitions.

Received: 24.01.2001
Revised: 20.06.2001

DOI: 10.4213/tmf315

 English version: Theoretical and Mathematical Physics, 2002, 130:3, 425–431

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