IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v92y2019i11d10.1140_epjb_e2019-100313-9.html
   My bibliography  Save this article

Adaptive cluster expansion for Ising spin models

Author

Listed:
  • Simona Cocco

    (Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris)

  • Giancarlo Croce

    (Sorbonne Université, CNRS, Institut de Biologie Paris Seine, Biologie computationnelle et quantitative – LCQB)

  • Francesco Zamponi

    (Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris)

Abstract

We propose an algorithm to obtain numerically approximate solutions of the direct Ising problem, that is, to compute the free energy and the equilibrium observables of spin systems with arbitrary two-spin interactions. To this purpose we use the Adaptive Cluster Expansion method [S. Cocco, R. Monasson, Phys. Rev. Lett. 106, 090601 (2011)], originally developed to solve the inverse Ising problem, that is, to infer the interactions from the equilibrium correlations. The method consists in iteratively constructing and selecting clusters of spins, computing their contributions to the free energy and discarding clusters whose contribution is lower than a fixed threshold. The properties of the cluster expansion and its performance are studied in detail on one dimensional, two dimensional, random and fully connected graphs with homogeneous or heterogeneous fields and couplings. We discuss the differences between different representations (Boolean and Ising) of the spin variables. Graphical abstract

Suggested Citation

  • Simona Cocco & Giancarlo Croce & Francesco Zamponi, 2019. "Adaptive cluster expansion for Ising spin models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(11), pages 1-17, November.
    • Handle: RePEc:spr:eurphb:v:92:y:2019:i:11:d:10.1140_epjb_e2019-100313-9
    DOI: 10.1140/epjb/e2019-100313-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1140/epjb/e2019-100313-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1140/epjb/e2019-100313-9?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.

    More about this item

    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:92:y:2019:i:11:d:10.1140_epjb_e2019-100313-9. 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.