IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v201y1993i4p581-592.html
   My bibliography  Save this article

High-temperature series analyses of the classical Heisenberg and XY models

Author

Listed:
  • Adler, Joan
  • Holm, Christian
  • Janke, Wolfhard

Abstract

Although there is now a good measure of agreement between Monte Carlo and high-temperature series expansion estimates for Ising (n = 1) models, published results for the critical temperature from series expansions up to 12th order for the three-dimensional classical Heisenberg (n = 3) and XY (n = 2) models do not agree very well with recent high-precision Monte Carlo estimates. In order to clarify this discrepancy we have analyzed extended high-temperature series expansions of the susceptibility, the second correlation moment, and the second field derivative of the susceptibility, which have been derived a few years ago by Lüscher and Weisz for general O(n) vector spin models on D-dimensional hypercubic lattices up to 14th order in K ≡ J/kBT. By analyzing these series expansions in three dimensions with two different methods that allow for confluent correction terms, we obtain good agreement with the standard field theory exponent estimates and with the critical temperatures estimates from the new high-precision Monte Carlo simulations. Furthermore, for the Heisenberg model we also reanalyze existing series for the susceptibility on the BCC lattice up to 11th order and on the FCC lattice up to 12th order using the same methods.

Suggested Citation

  • Adler, Joan & Holm, Christian & Janke, Wolfhard, 1993. "High-temperature series analyses of the classical Heisenberg and XY models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 201(4), pages 581-592.
    • Handle: RePEc:eee:phsmap:v:201:y:1993:i:4:p:581-592
    DOI: 10.1016/0378-4371(93)90130-V
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843719390130V
    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(93)90130-V?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. D'Onorio De Meo, M & Reger, J.D & Binder, K, 1995. "Critical behavior of diluted Heisenberg ferromagnets with competing interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 220(3), pages 628-647.
    2. de Sousa, J.Ricardo & de Albuquerque, Douglas F., 1997. "Critical properties of the classical XY and classical Heisenberg models: A renormalization group study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 236(3), pages 419-428.
    3. Brower, Richard & Orginos, Kostas & Shen, Yue & Tan, Chung-I, 1995. "Monte Carlo study of the Yukawa coupled two-spin Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(4), pages 554-564.
    4. Landau, D.P., 1994. "Computer simulation studies of critical phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 205(1), pages 41-64.

    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:201:y:1993:i:4:p:581-592. 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.