IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v436y2015icp547-557.html
   My bibliography  Save this article

Asymptotic behavior for a version of directed percolation on the honeycomb lattice

Author

Listed:
  • Chang, Shu-Chiuan
  • Chen, Lung-Chi

Abstract

We consider a version of directed bond percolation on the honeycomb lattice as a brick lattice such that vertical edges are directed upward with probability y, and horizontal edges are directed rightward with probabilities x and one in alternate rows. Let τ(M,N) be the probability that there is at least one connected-directed path of occupied edges from (0,0) to (M,N). For each x∈(0,1], y∈(0,1] and aspect ratio α=M/N fixed, we show that there is a critical value αc=(1−x+xy)(1+x−xy)/(xy2) such that as N→∞, τ(M,N) is 1, 0 and 1/2 for α>αc, α<αc and α=αc, respectively. We also investigate the rate of convergence of τ(M,N) and the asymptotic behavior of τ(MN−,N) and τ(MN+,N) where MN−/N↑αc and MN+/N↓αc as N↑∞.

Suggested Citation

  • Chang, Shu-Chiuan & Chen, Lung-Chi, 2015. "Asymptotic behavior for a version of directed percolation on the honeycomb lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 547-557.
    • Handle: RePEc:eee:phsmap:v:436:y:2015:i:c:p:547-557
    DOI: 10.1016/j.physa.2015.05.083
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437115004987
    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.2015.05.083?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:436:y:2015:i:c:p:547-557. 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.