Thermodynamic analysis of the three-state SOS model on the binary tree

Abstract

In this work, we investigate the thermodynamic properties of the three-state solid-on-solid (SOS) model on a binary Cayley tree. Employing recurrence relations, we analyze the partition function and derive explicit expressions for the local magnetization and the quadrupolar moment. One of the main results of the paper is the demonstration of the existence of a second-order phase transition in the model. To explore the system's dynamical behavior, we compute the Lyapunov exponent, which reveals transitions between distinct dynamical regimes. Our findings demonstrate the model's rich phase structure, characterized by the emergence of periodic regimes and the absence of chaos, as confirmed by Lyapunov analysis.