IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v620y2023ics037843712300331x.html
   My bibliography  Save this article

Ashkin–Teller model on a sequence of hierarchical lattices

Author

Listed:
  • Akimenko, S.S.
  • Myshlyavtsev, A.V.
  • Myshlyavtseva, M.D.

Abstract

Some hierarchical lattices are able to imitate Bravais lattices, and in some cases it is possible to obtain an exact solution. For example, on folded square hierarchical lattices (FSHLs) one can obtain an exact solution even for rather complicated models such as the two-layer Ising model. But this model has a simple behavior, so we chose a similar model with a much more diverse phase behavior. In this work, we have studied the Ashkin–Teller model on the first two representatives of the FSHLs family. An additional calculation was carried out on a square lattice by tensor renormalization group for a more visual comparison of the results. Based on the calculation results, we have constructed phase diagrams for symmetric and asymmetric cases. As expected, the diagrams are qualitatively the same for square and hierarchical lattices. There are areas with a noticeable deviation, but in some places the result corresponds to the exact solution. The second occurs only where the critical values of the model are determined by logarithms of algebraic numbers.

Suggested Citation

  • Akimenko, S.S. & Myshlyavtsev, A.V. & Myshlyavtseva, M.D., 2023. "Ashkin–Teller model on a sequence of hierarchical lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 620(C).
    • Handle: RePEc:eee:phsmap:v:620:y:2023:i:c:s037843712300331x
    DOI: 10.1016/j.physa.2023.128776
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843712300331X
    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.2023.128776?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:620:y:2023:i:c:s037843712300331x. 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.