IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v167y2023ics0960077922012656.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922012656
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2022.113086?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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).
    3. 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).
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ostilli, M., 2024. "Exact results for the Ising model on a small-world network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 641(C).
    2. Robson, Dominic T. & Annibale, Alessia & Baas, Andreas C.W., 2022. "Reproducing size distributions of swarms of barchan dunes on Mars and Earth using a mean-field model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    3. Caravelli, F., 2023. "On forest expansions for two-body partition functions on tree-like interaction graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    4. Barucca, Paolo, 2020. "Spectral density of equitable core–periphery graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    5. Barré, Julien & Gonçalves, Bruno, 2007. "Ensemble inequivalence in random graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 212-218.
    6. Anisimova, G.D. & Myshlyavtsev, A.V. & Akimenko, S.S., 2021. "The two-layer Ising model on a sequence of diamond-like hierarchical lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    7. Sun, Yi-Fan & Sun, Zheng-Yang, 2019. "Target observation of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 233-245.
    8. Pierre Paga & Reimer Kuhn, 2014. "Contagion in an interacting economy," Papers 1409.2625, arXiv.org, revised Mar 2015.
    9. Fabrizio Altarelli & Alfredo Braunstein & Luca Dall’Asta & Caterina De Bacco & Silvio Franz, 2015. "The Edge-Disjoint Path Problem on Random Graphs by Message-Passing," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-18, December.
    10. Yilun Shang, 2020. "Multi-Hop Generalized Core Percolation On Complex Networks," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-15, March.
    11. Correia, A.D. & Leestmaker, L.L. & Stoof, H.T.C. & Broere, J.J., 2022. "Asymmetric games on networks: Towards an Ising-model representation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    12. 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).
    13. Mukhamedov, Farrukh & Khakimov, Otabek, 2016. "Phase transition and chaos: P-adic Potts model on a Cayley tree," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 190-196.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922012656. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.