IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v92y1978i1p1-41.html
   My bibliography  Save this article

Transverse time-dependent spin correlation functions for the one-dimensional XY model at zero temperature

Author

Listed:
  • Vaidya, Hemant G.
  • Tracy, Craig A.

Abstract

We compute exactly the transverse time-dependent spin-spin correlation functions 〈Sx1(0)SxR+1(t)〉 and 〈Sy1(0)SyR+1(t)〉 at zero temperature for the one-dimensional XY model that is defined by the hamiltonian HN = - ΣNi=1 [(1 + γ)SxiSxi+1 + (1 − γ)SyiSyi+1 + hSzi]. We then analyze these correlation functions in two scaling limits: (a) γfixed, h → 1, R → ∞, t → ∞ such that ‖(h − 1)/γ‖[R2 − γ2t2]12 is fixed, and (b) h fixed less than one, γ → 0+, R → ∞, t → ∞ such that γ[R2 − (1 − h2)t2]12 is fixed. In these scaling regions we give both a perturbation expansion representation of the various scaling functions and we express these scaling functions in terms of a certain Painlevé transcendent of the third kind. From these representations we study both the small and large scaling variable limits in both the space-like and time-like regions.

Suggested Citation

  • Vaidya, Hemant G. & Tracy, Craig A., 1978. "Transverse time-dependent spin correlation functions for the one-dimensional XY model at zero temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 92(1), pages 1-41.
    • Handle: RePEc:eee:phsmap:v:92:y:1978:i:1:p:1-41
    DOI: 10.1016/0378-4371(78)90019-5
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437178900195
    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(78)90019-5?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:92:y:1978:i:1:p:1-41. 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.