The phase transition for the three-state SOS model with one-level competing interactions on the binary tree

TL;DR

This paper investigates a three-state SOS model with competing interactions on a binary tree, demonstrating phase transitions at certain parameters and establishing the absence of antiferromagnetic phases under specific conditions.

Contribution

It introduces a new analysis of phase transitions in a three-state SOS model with competing interactions on a Cayley tree, expanding understanding of such models.

Findings

Phase transition occurs at specific parameter values.

No antiferromagnetic phases under certain conditions.

Provides conditions for phase transition existence.

Abstract

In this paper, we consider a three-state solid-on-solid (SOS) model with two competing interactions (nearest-neighbour, one-level next-nearest-neighbour) on the Cayley tree of order two. We show that at some values of parameters the model exhibits a phase transition. We prove that for the model under some conditions there is no antiferromagnetic phases.