IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v391y2012i12p3417-3423.html
   My bibliography  Save this article

Cayley Trees and Bethe Lattices: A concise analysis for mathematicians and physicists

Author

Listed:
  • Ostilli, M.

Abstract

We review critically the concepts and the applications of Cayley Trees and Bethe Lattices in statistical mechanics in a tentative effort to remove widespread misuse of these simple, but yet important–and different–ideal graphs. We illustrate, in particular, two rigorous techniques to deal with Bethe Lattices, based respectively on self-similarity and on the Kolmogorov consistency theorem, linking the latter with the Cavity and Belief Propagation methods, more known to the physics community.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:12:p:3417-3423
    DOI: 10.1016/j.physa.2012.01.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112000647
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2012.01.038?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. 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).
    3. 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.
    4. 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).

    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:phsmap:v:391:y:2012:i:12:p:3417-3423. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.