IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v152y1988i3p343-358.html
   My bibliography  Save this article

The application of the differential operator method to the Blume-Emery-Griffiths model

Author

Listed:
  • Kaneyoshi, T.
  • Sarmento, E.F.

Abstract

Within an effective-field approximation, general expressions for evaluating the second-order phase transition line and the tricritical point of the anisotropic Blume-Emery-Griffiths model are obtained by the use of the differential operator technique. The phase diagrams and the behavior of the tricritical point are investigated numerically for the honeycomb lattice (z = 3) and square lattice (z = 4). We find a new disordered phase which may correspond to the staggered quadrupolar phase predicted in the Monte Carlo simulation, when some conditions are satisfied. The phase diagrams for z = 3 and z = 4 systems exhibit a reentrant behavior for positive values of the uniaxial anisotropy parameter. The change of the tricritical point with the value of the reduced biquadratic parameter is also studied for the system with z = 3.

Suggested Citation

  • Kaneyoshi, T. & Sarmento, E.F., 1988. "The application of the differential operator method to the Blume-Emery-Griffiths model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 152(3), pages 343-358.
    • Handle: RePEc:eee:phsmap:v:152:y:1988:i:3:p:343-358
    DOI: 10.1016/0378-4371(88)90192-6
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437188901926
    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(88)90192-6?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. Siqueira, A.F. & Fittipaldi, I.P., 1986. "New effective-field theory for the Blume-Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 138(3), pages 592-611.
    2. De Alcantara Bonfim, O.F., 1985. "Mean field renormalization group analysis of the Blume-Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 130(1), pages 367-373.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kaneyoshi, T., 1990. "Surface tricritical behavior of a semi-infinite Ising model with a spin-one free surface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 163(2), pages 533-544.
    2. Kaneyoshi, T., 1991. "Surface phase diagrams of a spin-one monolayer on a semi-infinite spin-12 Ising ferromagnet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(2), pages 389-400.
    3. Wang, Xuan-Zhang & Zhao, Yan, 1993. "Phase diagrams of transverse Ising film," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 193(1), pages 133-140.
    4. Kaneyoshi, T., 1990. "Correlated-effective-field treatment of spin-one ising models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 164(3), pages 730-750.

    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. Kaneyoshi, T., 1990. "Correlated-effective-field treatment of spin-one ising models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 164(3), pages 730-750.
    2. Rocha-Neto, Mário J.G. & Camelo-Neto, G. & Nogueira Jr., E. & Coutinho, S., 2018. "The Blume–Capel model on hierarchical lattices: Exact local properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 559-573.
    3. Idogaki, Toshihiro & Uryû, Norikiyo, 1992. "A new effective field theory for the anisotropic Heisenberg ferromagnet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 181(1), pages 173-186.
    4. Kaneyoshi, T., 1989. "Magnetic properties of the mixed spin system with a random crystal field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 155(3), pages 460-474.
    5. Jurčišinová, E. & Jurčišin, M., 2016. "Spin-1 Ising model on tetrahedron recursive lattices: Exact results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 554-568.
    6. Schmidt, M. & Dias, P.F., 2021. "Correlated cluster mean-field theory for Ising-like spin systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    7. Chen, Shyh-Tzer, 1996. "Mean-field renormalization group for the q-state clock spin-glass model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 229(2), pages 181-187.
    8. Kaneyoshi, T., 1994. "Tricritical behavior of a mixed spin-12 and spin-2 Ising system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 205(4), pages 677-686.
    9. Jurčišinová, E. & Jurčišin, M., 2016. "Exact results for the spin-1 Ising model on pure “square” Husimi lattices: Critical temperatures and spontaneous magnetization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 641-653.
    10. Verona de Resende, H.F. & SáBarreto, F.C. & Plascak, J.A., 1988. "Renormalization group treatment of the mixed-spin system in d-dimensional lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 149(3), pages 606-612.
    11. Kaneyoshi, T., 1990. "Surface tricritical behavior of a semi-infinite Ising model with a spin-one free surface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 163(2), pages 533-544.
    12. Jurčišin, M. & Bobák, A. & Jaščur, M., 1996. "Two-spin cluster theory for the Blume-Capel model with arbitrary spin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 224(3), pages 684-696.
    13. Kaneyoshi, T. & Tucker, J.W. & Jaščur, M., 1992. "Differential operator technique for higher spin problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 186(3), pages 495-512.
    14. Kaneyoshi, T., 1992. "A general theory of spin-one Ising models in the correlated effective-field approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 182(3), pages 436-454.

    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:152:y:1988:i:3:p:343-358. 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.