IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v289y2001i1p137-156.html
   My bibliography  Save this article

Exact eigenvalues of the Ising Hamiltonian in one-, two- and three-dimensions in the absence of a magnetic field

Author

Listed:
  • Dixon, J.M.
  • Tuszynski, J.A.
  • Nip, M.L.A.

Abstract

The Hamiltonian of the Ising model in one-, two- and three-dimensions has been analysed using unitary transformations and combinatorics. We have been able to obtain closed formulas for the eigenvalues of the Ising Hamiltonian for an arbitrary number of dimensions and sites. Although the solution provided assumes the absence of external magnetic fields an extension to include a magnetic field along the z-axis is readily extracted. Furthermore, generalisations to a higher number of spin components on each site are possible within this method. We made numerical comparisons with the partition function from the earlier analytical expressions known in the literature for one- and two-dimensional cases. We find complete agreement with these studies.

Suggested Citation

  • Dixon, J.M. & Tuszynski, J.A. & Nip, M.L.A., 2001. "Exact eigenvalues of the Ising Hamiltonian in one-, two- and three-dimensions in the absence of a magnetic field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(1), pages 137-156.
  • Handle: RePEc:eee:phsmap:v:289:y:2001:i:1:p:137-156
    DOI: 10.1016/S0378-4371(00)00318-6
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437100003186
    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/S0378-4371(00)00318-6?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. Dixon, J.M. & Tuszyński, J.A. & Carpenter, E.J., 2005. "Analytical expressions for energies, degeneracies and critical temperatures of the 2D square and 3D cubic Ising models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 487-510.
    2. Leonid Litinskii & Boris Kryzhanovsky, 2021. "Inverse Problem for Ising Connection Matrix with Long-Range Interaction," Mathematics, MDPI, vol. 9(14), pages 1-11, July.
    3. Litinskii, L.B. & Kryzhanovsky, B.V., 2020. "Eigenvalues of Ising connection matrix with long-range interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).

    More about this item

    Keywords

    ; ; ;
    All these keywords.

    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:289:y:2001:i:1:p:137-156. 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.