On $p$-adic Gibbs measures for the SOS model on a Cayley tree

TL;DR

This paper investigates the properties of $p$-adic Gibbs measures for the SOS model with multiple states on a Cayley tree, exploring their mathematical structure and potential implications in statistical mechanics.

Contribution

It introduces a new analysis of $p$-adic Gibbs measures for the SOS model on Cayley trees, extending previous real-valued models to the $p$-adic setting.

Findings

Existence conditions for $p$-adic Gibbs measures

Characterization of phase transitions in the $p$-adic context

Mathematical properties of the $p$-adic SOS model

Abstract

We consider $m+1$-state $p$-adic SOS model on a Cayley tree of order $k$.