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A new approach to studying the thermodynamic properties of the q-state Potts model on a Cayley tree

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  • Akın, Hasan
  • Ulusoy, Suleyman

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.

Suggested Citation

  • Akın, Hasan & Ulusoy, Suleyman, 2023. "A new approach to studying the thermodynamic properties of the q-state Potts model on a Cayley tree," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007129
    DOI: 10.1016/j.chaos.2023.113811
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    References listed on IDEAS

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    1. Ostilli, M., 2012. "Cayley Trees and Bethe Lattices: A concise analysis for mathematicians and physicists," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3417-3423.
    2. Türkoğlu, Alpar & Berker, A. Nihat, 2021. "Phase transitions of the variety of random-field Potts models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    3. Selman Uguz & Nasir Ganikhodjaev & Hasan Akin & Seyit Temir, 2012. "Lyapunov Exponents And Modulated Phases Of An Ising Model On Cayley Tree Of Arbitrary Order," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 23(05), pages 1-15.
    4. Bornholdt, Stefan, 2022. "A q-spin Potts model of markets: Gain–loss asymmetry in stock indices as an emergent phenomenon," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
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