IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v87y2014i3p1-1310.1140-epjb-e2014-40952-4.html
   My bibliography  Save this article

Mean field bipartite spin models treated with mechanical techniques

Author

Listed:
  • Adriano Barra
  • Andrea Galluzzi
  • Francesco Guerra
  • Andrea Pizzoferrato
  • Daniele Tantari

Abstract

Inspired by a continuously increasing interest in modeling and framing complex systems in a thermodynamic rationale, in this paper we continue our investigation in adapting well-known techniques (originally stemmed in fields of physics and mathematics far from the present) for solving for the free energy of mean field spin models in a statistical mechanics scenario. Focusing on the test cases of bipartite spin systems embedded with all the possible interactions (self and reciprocal), we show that both the fully interacting bipartite ferromagnet, as well as the spin glass counterpart, at least at the replica symmetric level, can be solved via the fundamental theorem of calculus, trough an analogy with the Hamilton-Jacobi theory and lastly with a mapping to a Fourier diffusion problem. All these technologies are shown symmetrically for ferromagnets and spin-glasses in full details and contribute as powerful tools in the investigation of complex systems. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Adriano Barra & Andrea Galluzzi & Francesco Guerra & Andrea Pizzoferrato & Daniele Tantari, 2014. "Mean field bipartite spin models treated with mechanical techniques," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(3), pages 1-13, March.
    • Handle: RePEc:spr:eurphb:v:87:y:2014:i:3:p:1-13:10.1140/epjb/e2014-40952-4
    DOI: 10.1140/epjb/e2014-40952-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1140/epjb/e2014-40952-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1140/epjb/e2014-40952-4?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. Alemanno, Francesco & Camanzi, Luca & Manzan, Gianluca & Tantari, Daniele, 2023. "Hopfield model with planted patterns: A teacher-student self-supervised learning model," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    2. Elena Agliari & Adriano Barra & Andrea Galluzzi & Marco Alberto Javarone & Andrea Pizzoferrato & Daniele Tantari, 2015. "Emerging Heterogeneities in Italian Customs and Comparison with Nearby Countries," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-24, December.

    More about this item

    Keywords

    Statistical and Nonlinear Physics;

    Statistics

    Access and download statistics

    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:spr:eurphb:v:87:y:2014:i:3:p:1-13:10.1140/epjb/e2014-40952-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.