IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v306y2002icp98-106.html
   My bibliography  Save this article

Critical behavior of spin and polymer models with aperiodic interactions

Author

Listed:
  • Haddad, T.A.S.
  • Salinas, S.R.

Abstract

We review and extend some recent investigations of the effects of aperiodic interactions on the critical behavior of ferromagnetic q-state Potts models. By considering suitable diamond or necklace hierarchical lattices, and assuming a distribution of interactions according to a class of two-letter substitution rules, the problem can be formulated in terms of recursion relations in parameter space. The analysis of stability of the fixed points leads to an exact criterion to gauge the relevance of geometric fluctuations. For irrelevant fluctuations, the critical behavior remains unchanged with respect to the uniform systems. For relevant fluctuations, there appears a two-cycle of saddle-point character in parameter space. A scaling analysis, supported by direct numerical thermodynamic calculations, shows the existence of novel critical universality classes associated with relevant geometric fluctuations. Also, we show that similar qualitative results are displayed by a simple model of two directed polymers on a diamond hierarchical structure with aperiodic bond interactions.

Suggested Citation

  • Haddad, T.A.S. & Salinas, S.R., 2002. "Critical behavior of spin and polymer models with aperiodic interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 306(C), pages 98-106.
    • Handle: RePEc:eee:phsmap:v:306:y:2002:i:c:p:98-106
    DOI: 10.1016/S0378-4371(02)00489-2
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437102004892
    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)00489-2?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:306:y:2002:i:c:p:98-106. 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.