IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v461y2016icp554-568.html
   My bibliography  Save this article

Spin-1 Ising model on tetrahedron recursive lattices: Exact results

Author

Listed:
  • Jurčišinová, E.
  • Jurčišin, M.

Abstract

We investigate the ferromagnetic spin-1 Ising model on the tetrahedron recursive lattices. An exact solution of the model is found in the framework of which it is shown that the critical temperatures of the second order phase transitions of the model are driven by a single equation simultaneously on all such lattices. It is also shown that this general equation for the critical temperatures is equivalent to the corresponding polynomial equation for the model on the tetrahedron recursive lattice with arbitrary given value of the coordination number. The explicit form of these polynomial equations is shown for the lattices with the coordination numbers z=6, 9, and 12. In addition, it is shown that the thermodynamic properties of all possible physical phases of the model are also completely driven by the corresponding single equations simultaneously on all tetrahedron recursive lattices. In this respect, the spontaneous magnetization, the free energy, the entropy, and the specific heat of the model are studied in detail.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:461:y:2016:i:c:p:554-568
    DOI: 10.1016/j.physa.2016.06.049
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711630317X
    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.2016.06.049?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. Chakraborty, K.G. & Tucker, J.W., 1986. "Statistical mechanics of a spin-one Ising model on a Bethe lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 137(1), pages 122-136.
    2. 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.
    3. Kaneyoshi, T., 2000. "Decoupling approximation in spin-S(S≧1/2) Ising systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 286(3), pages 518-530.
    4. Ananikian, N.S. & Izmailian, N.Sh. & Oganessyan, K.A., 1998. "An Ising spin-S model on generalized recursive lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 207-214.
    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. 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.
    2. 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.
    3. 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.
    4. Jurčišinová, E. & Jurčišin, M., 2019. "Applicability of effective field theory cluster approximations for investigation of geometrically frustrated magnetic systems: Antiferromagnetic model on kagome lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 644-657.
    5. 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.
    6. Jurčišinová, E. & Jurčišin, M., 2019. "Relevance of recursive lattice approximations for description of frustrated magnetic systems: Star kagome-like recursive lattice approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 330-351.
    7. 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.
    8. 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).
    9. Jurčišinová, E. & Jurčišin, M., 2014. "The first order phase transitions in the multisite spin-1/2 model on a pure Husimi lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 375-385.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Jurčišinová, E. & Jurčišin, M., 2017. "Evidence for the ferromagnetic frustration in a classical spin-1∕2 system with multisite interaction in external magnetic field: Exact results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 296-317.

    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:461:y:2016:i:c:p:554-568. 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.