Geodesic
$\mathbb {Z}$Existence of a Phase Transition for the Potts $p$-adic Model on the Set $\mathbb {Z}$
Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 3, pp. 500-507

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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. 
@article{TMF_2002_130_3_a8,
     author = {N. N. Ganikhodzhaev and F. M. Mukhamedov and U. A. Rozikov},
     title = {$\mathbb {Z}${Existence} of a {Phase} {Transition} for the {Potts} $p$-adic {Model} on the {Set} $\mathbb {Z}$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {130},
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     year = {2002},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2002_130_3_a8/}
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N. N. Ganikhodzhaev; F. M. Mukhamedov; U. A. Rozikov. $\mathbb {Z}$Existence of a Phase Transition for the Potts $p$-adic Model on the Set $\mathbb {Z}$. Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 3, pp. 500-507. http://geodesic.mathdoc.fr/item/TMF_2002_130_3_a8/