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The classification of disordered phases of mixed spin (2,1/2) Ising model and the chaoticity of the corresponding dynamical system

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  • Akın, Hasan

Abstract

We study an Ising model having the mixed spins {±1/2} and {±2,±1,0} on Cayley tree of second-order. We construct the Gibbs measures corresponding to the model and classify the disordered phases associated to the Gibbs measures. Using the compatibility condition, we obtain the system of functional equations associated with the model. Contrary to the Ising model with two different neighbor interactions, we prove that for the given model, the phase transition phenomenon occurs in both the antiferromagnetic and antiferromagnetic regions. Stability analysis of the dynamic system associated with the model is performed at the obtained fixed point. By calculating the Lyapunov exponent numerically, we show that the corresponding dynamical system exhibits the chaotic behavior in some regions. We identify regions where the disordered phases are extreme by means of a tree-indexed Markov chain. We satisfy the Kesten–Stigum condition for non-extremality of the disordered phase according to the fixed point.

Suggested Citation

  • Akın, Hasan, 2023. "The classification of disordered phases of mixed spin (2,1/2) Ising model and the chaoticity of the corresponding dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922012656
    DOI: 10.1016/j.chaos.2022.113086
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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. M. Mézard & G. Parisi, 2001. "The Bethe lattice spin glass revisited," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(2), pages 217-233, March.
    3. Albayrak, Erhan, 2020. "The study of mixed spin-1 and spin-1/2: Entropy and isothermal entropy change," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    4. Jabar, A. & Masrour, R., 2020. "Magnetic properties on a decorated triangular lattice: A Monte Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
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