IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i22p5604-5614.html
   My bibliography  Save this article

Study of two dimensional anisotropic Ising models via a renormalization group approach

Author

Listed:
  • Taherkhani, Farid
  • Akbarzadeh, Hamed
  • Abroshan, Hadi
  • Ranjbar, Shahram
  • Fortunelli, Alessandro
  • Parsafar, Gholamabbas

Abstract

A method is developed to calculate the critical line of two dimensional (2D) anisotropic Ising model including nearest-neighbor interactions. The method is based on the real-space renormalization group (RG) theory with increasing block sizes. The reduced temperatures, Ks (where K=JkBT and J, kB, and T are the spin coupling interaction, the Boltzmann constant, and the absolute temperature, respectively), are calculated for different block sizes. By increasing the block size, the critical line for three types of lattice, namely: triangular, square, and honeycomb, is obtained and found to compare well with corresponding results reported by Onsager in the thermodynamic limit. Our results also show that, for the investigated lattices, there exist asymptotic limits for the critical line. Finally the critical exponents are obtained, again in good agreement with Onsager’s results. We show that the magnitude of the spin coupling interaction with anisotropic ferromagnetic characteristics does not change the values of the critical exponents, which stay constant along the direction of the critical line.

Suggested Citation

  • Taherkhani, Farid & Akbarzadeh, Hamed & Abroshan, Hadi & Ranjbar, Shahram & Fortunelli, Alessandro & Parsafar, Gholamabbas, 2013. "Study of two dimensional anisotropic Ising models via a renormalization group approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5604-5614.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:22:p:5604-5614
    DOI: 10.1016/j.physa.2013.07.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113006365
    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/j.physa.2013.07.026?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:392:y:2013:i:22:p:5604-5614. 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.