The author previously investigated the thermodynamic properties of the one-dimensional Potts-SOS model on the lattice of positive natural numbers N in [Akin H, Phys. Scr. 99 (2024), 055231]. In this present paper, we extend that research by determining the Gibbs measures for the same mixed-type model using partition functions constructed on a second-order semi-infinite Cayley tree. By leveraging the self-similarity of the Cayley tree, we analyze the behavior of these partition functions and identify the regions where phase transitions occur. We pinpoint these phase transition regions through a stability analysis of the dynamical system associated with the model at specific fixed points.
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Hasan Akın (2024) studied this question.
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