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New effective-field theory for the Blume-Capel model

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  • Siqueira, A.F.
  • Fittipaldi, I.P.

Abstract

A new type of effective-field theory that has recently been used with success for many applications concerning the usual two-state Ising model is herein extended to the Blume-Capel model. The method, which can explicitly and systematically include correlation effects, is illustrated in several lattice structures by employing its simplest approximate version, in which spin-spin correlations are neglected. It is shown that this approximative procedure, although analytically simple, provides in particular a vanishing critical temperature for one-dimensional systems and leads to results quite superior to those currently obtained within the Molecular Field Approximation for higher-dimensional systems. Within this framework we discuss as functions of temperature and for any values of the anisotropy parameter D, the order parameter, the thermal average of the square of the single-site spin variable, the internal energy and the specific heat as well as the ferromagnetic-phase stability limit. Whenever comparison is possible a satisfactory qualitative (and to a certain extent quantitative) agreement is observed with results available in the literature in which more sophisticated treatments are used. In particular, our result for the tricritical point at which the system exhibits a first-order phase transition is in quite good agreement with those obtained by using Series Expansion Methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:138:y:1986:i:3:p:592-611
    DOI: 10.1016/0378-4371(86)90035-X
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    Citations

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    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. & 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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).
    12. 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.
    13. 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.

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