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Phase Transition Analysis of the Potts-SOS Model with Spin Set {-1,0, 1} on the Cayley Tree
Version 1
: Received: 23 August 2024 / Approved: 23 August 2024 / Online: 26 August 2024 (03:02:46 CEST)
How to cite: Akin, H. Phase Transition Analysis of the Potts-SOS Model with Spin Set {-1,0, 1} on the Cayley Tree. Preprints 2024, 2024081768. https://doi.org/10.20944/preprints202408.1768.v1 Akin, H. Phase Transition Analysis of the Potts-SOS Model with Spin Set {-1,0, 1} on the Cayley Tree. Preprints 2024, 2024081768. https://doi.org/10.20944/preprints202408.1768.v1
Abstract
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.
Keywords
Potts-SOS model; Gibbs measure; phase transition; stability analysis
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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