Phase transition analysis of the Potts-SOS model with spin set {−1,0,+1} on the Cayley tree

Abstract

Recently, the Potts-SOS model on Cayley trees was studied using the Kolmogorov consistency condition to investigate the existence and properties of Gibbs measures. The author previously examined the thermodynamic properties of the one-dimensional Potts-SOS model on the positive natural number lattice \( \mathbb{N} \), demonstrating the absence of phase transitions [Akin H, Phys. Scr. 99 (2024), 055231]. In this study, we apply the cavity method to explore the non-uniqueness of Gibbs measures for the Potts-SOS model with spins $\{-1,0,+1\}$ on a second-order semi-infinite Cayley tree. We address the phase transition problem by analyzing the model's iterative equation system and perform stability analysis at fixed points to determine regions where phase transitions occur.