IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v230y1996i1p19-26.html
   My bibliography  Save this article

Critical behavior of nonlinear random conductance networks: Real-space renormalization group approach

Author

Listed:
  • Siu, Wing-Hon

Abstract

The real-space renormalization group theory is used to study the critical behavior of nonlinear random conductance networks in two and three dimensions, in which the components obey a current-voltage (I – V) relation of the form I = χμVγ with γ > 0 and μ = i,m where i,m represent the inclusion of volume fraction p and the host medium of volume fraction q (p + q = 1), respectively. Two important limits are worth studying: (1) normal conductor-insulator (N/I) mixture (χm = 0) and (2) superconductor-normal conductor (S/N) mixture (χm = ∞). As the percolation threshold pc (or qc) is approached, the effective nonlinear response χe is found to behave as χe ≈ (p − pc)t in the N/I limit while χe ≈ (qc − q)−s in the S/N limit. We calculate the critical exponents t and s as a function of γ. A more general duality relation is found to obey in two dimensions. By a connection with the links-nodes-blobs picture, t and s can be related to critical exponents ζR and ζs, which describe the geometry of the percolating network. The results are compared with those of the series analysis and excellent agreements are found over a wide range of γ.

Suggested Citation

  • Siu, Wing-Hon, 1996. "Critical behavior of nonlinear random conductance networks: Real-space renormalization group approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(1), pages 19-26.
    • Handle: RePEc:eee:phsmap:v:230:y:1996:i:1:p:19-26
    DOI: 10.1016/0378-4371(96)00060-X
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843719600060X
    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(96)00060-X?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:230:y:1996:i:1:p:19-26. 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.