IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v309y2002i1p69-78.html
   My bibliography  Save this article

Existence of the upper critical dimension of the Kardar–Parisi–Zhang equation

Author

Listed:
  • Katzav, Eytan
  • Schwartz, Moshe

Abstract

The controversy whether or not the Kardar–Parisi–Zhang (KPZ) equation has an upper critical dimension (UCD) is going on for quite a long time. Some approximate integral equations for the two-point function served as an indication for the existence of a UCD, by obtaining a dimension, above which the equation does not have a strong coupling solution. A surprising aspect of these studies, however, is that various authors who considered the same equation produced large variations in the UCD. This caused some doubts concerning the existence of a UCD. Here we revisit these calculations, describe the reason for such large variations in the results of identical calculations, show by a large-d asymptotic expansion that indeed there exists a UCD and then obtain it numerically by properly defining the integrals involved. Since many difficult problems in condensed matter physics of non-linear nature are handled with mode-coupling and self-consistent theories, this work might also contribute to other researchers working on a large class of different problems that might run into the same inconsistencies.

Suggested Citation

  • Katzav, Eytan & Schwartz, Moshe, 2002. "Existence of the upper critical dimension of the Kardar–Parisi–Zhang equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(1), pages 69-78.
    • Handle: RePEc:eee:phsmap:v:309:y:2002:i:1:p:69-78
    DOI: 10.1016/S0378-4371(02)00553-8
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437102005538
    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(02)00553-8?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. Wang, Chuan & Xia, Hui, 2024. "Scaling properties and height distributions of persisting roughness in the discrete growth models in the presence of the angle of repose," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

    More about this item

    Keywords

    KPZ equation; Upper critical dimension;

    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:309:y:2002:i:1:p:69-78. 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.