IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v97y1979i1p75-103.html
   My bibliography  Save this article

Qualitative theory of three-dimensional rotator model

Author

Listed:
  • Holz, A.

Abstract

The 3-dimensional planar rotator (PR) model with short-range interaction is studied in the “harmonic” approximation where spin wave and vortex loop (VL) system decouple. The phase transition (PT) occuring in the PR-model is studied via the correlation and stability properties of the VL-system for which a tentative phase diagram is set up. Under the assumption that the PT of the PR-model is continuous an ansatz for the “dielectric” function ϵq of the VL-system is made which leads at criticality simultaneously to scaling of the VL-system and of the PR-model. Physical arguments are given to justify the dimensional properties of ϵq which led to this result. The critical exponents for the VL-system in usual notation are ηL=1, and γL=vL=0. The latter represent logarithmic singularities, i.e., ϵ0∼–ln|τ|zγ, and κ∼–1/ln|τ|zv. The critical expon ents of the PR-model can be expressed in terms of those of the VL-system. The low and high-temperature correlation functions are given. It is shown that only in the presence of an anisotropy field, e.g., a magnetic field, the low temperature correlation function decays exponentially. The relation between the PR-model, and the melting of crystals is briefly discussed.

Suggested Citation

  • Holz, A., 1979. "Qualitative theory of three-dimensional rotator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 97(1), pages 75-103.
    • Handle: RePEc:eee:phsmap:v:97:y:1979:i:1:p:75-103
    DOI: 10.1016/0378-4371(79)90081-5
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437179900815
    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(79)90081-5?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:97:y:1979:i:1:p:75-103. 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.