The qualitative properties of 1D mixed-type Potts-SOS model with 1-spin and its dynamical behavior

Abstract

In this investigation, we consider the one-dimensional (1D) mixed-type Potts-SOS model, where the spin is within the range of $\{-1, 0, 1\}$. We elaborate thermodynamic characteristics of 1D Potts-SOS model through the application of three distinct analytical approaches. We provide a brief overview of all translation-invariant splitting Gibbs measures (TISGMs) applicable to this model. For the model with a boundary field condition, we provide a comprehensive analysis of the uniqueness and non-uniqueness properties of the subset of fully homogeneous splitting Gibbs masures (SGMs). Our demonstration reveals that the model under consideration does not exhibit a phase transition phenomenon. We are also curious in the stability study of the suggested fixed points associated with the Gibbs measures. We show that the magnetization decreases to zero. By means of the transfer matrix method, we compute the free energy, entropy and internal energy of the model.