Geodesic
$p$-Adic solid-on-solid model on a~Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 3, pp. 547-562

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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. 
@article{TMF_2017_193_3_a12,
     author = {O. N. Khakimov},
     title = {$p${-Adic} solid-on-solid model on {a~Cayley} tree},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {547--562},
     publisher = {mathdoc},
     volume = {193},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_193_3_a12/}
}
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O. N. Khakimov. $p$-Adic solid-on-solid model on a~Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 3, pp. 547-562. http://geodesic.mathdoc.fr/item/TMF_2017_193_3_a12/