IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v258y1998i1p32-44.html
   My bibliography  Save this article

Phase diagram of a stochastic cellular automaton with long-range interactions

Author

Listed:
  • Cannas, Sergio A.

Abstract

A stochastic one-dimensional cellular automaton with long range spatial interactions is introduced. In this model the state probability of a given site at time t depends on the state of all the other sites at time t−1 through a power law of the type 1/rα, r being the distance between sites. For α→∞ this model reduces to the Domany–Kinzel cellular automaton. The dynamical phase diagram is analyzed using Monte Carlo simulations for 0⩽α⩽∞. We found the existence of two different regimes: one for 0⩽α⩽1 and the other for α>1. It is shown that in the first regime the phase diagram becomes independent of α. Regarding the frozen-active phase transition in this regime, a strong evidence is found that the mean-field prediction for this model becomes exact, a result already encountered in magnetic systems. It is also shown that, for replicas evolving under the same noise, the long-range interactions fully suppress the spreading of damage for 0⩽α⩽1.

Suggested Citation

  • Cannas, Sergio A., 1998. "Phase diagram of a stochastic cellular automaton with long-range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 258(1), pages 32-44.
    • Handle: RePEc:eee:phsmap:v:258:y:1998:i:1:p:32-44
    DOI: 10.1016/S0378-4371(98)00270-2
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437198002702
    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/S0378-4371(98)00270-2?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.

    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:258:y:1998:i:1:p:32-44. 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.