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Phase diagrams of the Blume-Emery-Griffiths model: real-space renormalization group investigation and finite size scaling analysis

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  • Bakchich, A.
  • Benyoussef, A.
  • Touzani, M.

Abstract

An approximate real-space renormalization group scheme based on the Migdal-Kadanoff recursion relations and the finite size scaling method are used to study the phase diagrams of the two-dimensional spin-1 Ising model with nearest-neighbor interactions, both bilinear and biquadratic, and with a crystal-field interaction. Contrary to previous studies, we clarify the behavior of the model at low temperature including the region J + K < 0 and Δ<0, where a staggered quadrupolar phase appears. With both methods we show that the staggered quadrupolar and the ferromagnetic phases are separated by a disordered phase, and the second-order phase boundary lines of the two ordered phases meet only at zero temperature.

Suggested Citation

  • Bakchich, A. & Benyoussef, A. & Touzani, M., 1992. "Phase diagrams of the Blume-Emery-Griffiths model: real-space renormalization group investigation and finite size scaling analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 186(3), pages 524-533.
    • Handle: RePEc:eee:phsmap:v:186:y:1992:i:3:p:524-533
    DOI: 10.1016/0378-4371(92)90214-B
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    1. Griffiths, Mary, 1977. "Nutrition : Second European nutrition conference, Munich, 14-17 September 1976," Food Policy, Elsevier, vol. 2(1), pages 76-77, February.
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    Cited by:

    1. Bakchich, A. & Benyoussef, A. & Touzani, M., 1993. "Antiferromagnetic Potts model in a magnetic field: a finite size scaling study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 192(3), pages 516-524.
    2. Grigelionis, Gintautas & Rosengren, Anders, 1994. "Study of the Blume-Emery-Griffiths model on the triangular lattice by the cluster-variation method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(2), pages 287-299.

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