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

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  • 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
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    References listed on IDEAS

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    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.
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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. 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.
    3. 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.
    4. 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.

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