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

We consider a p-adic solid-on-solid (SOS) model with a nearest-neighbor coupling, m+1 spins, and a coupling constant J ∈ 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 | 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.

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