IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v160y1989i3p298-309.html
   My bibliography  Save this article

Scaling properties of eden clusters in three and four dimensions

Author

Listed:
  • Devillard, Pierre
  • Stanley, H.Eugene

Abstract

We study the scaling properties of noise reduced Eden clusters in three and four dimensions for variant B in the strip geometry. We find that the width W for large times behaves as a(s)g(Lsd−1), where L is the width of the strip, s the noise reduction parameter, d the dimension of space, and a(s) a decreasing function of s, g is a scaling function with the property g(u)→12 as u→0 and g(u)∼ux as u→∞, where χ is the roughness exponent. This scaling result leads to a new way of determining χ. In 3 dimensions, our numerical values for χ support a recent conjecture by Kim and Kosterlitz: χ = 2(d + 2), and contradict all the former analytical conjectures. In 4 dimensions, we cannot distinguish between the conjectures of Kim and Kosterlitz and the conjecture of Wolf and Kertész, because large crossovers and finite size effects make the measurement of the exponents difficult.

Suggested Citation

  • Devillard, Pierre & Stanley, H.Eugene, 1989. "Scaling properties of eden clusters in three and four dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 160(3), pages 298-309.
    • Handle: RePEc:eee:phsmap:v:160:y:1989:i:3:p:298-309
    DOI: 10.1016/0378-4371(89)90444-5
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437189904445
    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/10.1016/0378-4371(89)90444-5?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:eee:phsmap:v:160:y:1989:i:3:p:298-309. 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.