IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v211y1994i1p124-146.html
   My bibliography  Save this article

A spin-S model on a Bethe lattice

Author

Listed:
  • Tamashiro, M.N.
  • Salinas, S.R.A.

Abstract

We present an exact formulation of an Ising spin-S model on a Cayley tree as a 2S-dimensional nonlinear discrete map. The attractors of the map are associated with the thermodynamic solutions on a Bethe lattice. We analyse in detail the typical half-integer case S = 32, with bilinear interactions and the inclusion of a crystal field. There is a stable paramagnetic fixed point at high temperatures. There is also a low-temperature region of stability of two distinct ferromagnetic fixed points. In addition to these usual attractors, we detect the presence of several unstable fixed points, which are however irrelevant to the thermodynamic behavior. In the limit of infinite coordination of the tree, the problem is simplified and we regain the standard results of a mean-field approximation. For S = 32, with biquadratic interactions but no crystal field, we confirm the existence of a ferrimagnetic phase for finite coordinations of the tree and analyse the occurrence of re-entrant boundaries inside the ordered region. For the typical integer spin case S = 2, without biquadratic interactions, we show the splitting of the first-order paramagnetic boundary, in agreement with mean-field calculations. Also, we confirm the existence of a ferrimagnetic phase in the S = 1 case for negative biquadratic interactions.

Suggested Citation

  • Tamashiro, M.N. & Salinas, S.R.A., 1994. "A spin-S model on a Bethe lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 211(1), pages 124-146.
  • Handle: RePEc:eee:phsmap:v:211:y:1994:i:1:p:124-146
    DOI: 10.1016/0378-4371(94)90073-6
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437194900736
    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(94)90073-6?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.

    References listed on IDEAS

    as
    1. Coutinho, S. & SáBarreto, F.C. & Vasconcelos dos Santos, R.J., 1993. "Ising model randomly decorated with general spin angular momentum," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 196(3), pages 461-475.
    2. Carneiro, C.E.I. & Henriques, V.B. & Salinas, S.R., 1989. "On the equivalence of different Landau expansions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 162(1), pages 88-98.
    3. Nihat Berker, A., 1993. "Critical behavior induced by quenched disorder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 194(1), pages 72-76.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Borelli, M.E.S. & Carneiro, C.E.I., 1996. "Global mean-field phase diagram of the spin-1 Ising ferromagnet in a random crystal field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(1), pages 249-256.
    2. Türkoğlu, Alpar & Berker, A. Nihat, 2021. "Phase transitions of the variety of random-field Potts models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    3. Laaboudi, B. & Kerouad, M., 1997. "The Blume-Capel model with four-spin interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(3), pages 729-736.

    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:211:y:1994:i:1:p:124-146. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.