A new approach to studying the thermodynamic properties of the [formula omitted]-state Potts model on a Cayley tree

Abstract

The present paper extends the work of Akın and Ulusoy (2022). On a Cayley tree of order k with zero effective local external fields, we analyze the q-state Potts model (q-SPM) in the presence of competing for two nearest interactions and prolonged next nearest interactions. We establish Gibbs measures for the model using the Cayley tree’s self-similarity feature. The model’s phase transitions problem has been completely solved. Indeed, the critical surfaces that indicate the model’s phase transition are computed. There is a phase transition above this critical surface, and there is a single Gibbs measure found elsewhere. The chaoticity of the phases (Gibbs measures) is investigated using Lyapunov exponents. We analyze some of the q-SPM’s thermodynamic features. Using the cavity approach, we calculate the model’s free energy and entropy.