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Metastable and unstable states of the Blume–Capel model obtained by the cluster variation method and the path probability method

Author

Listed:
  • Ekiz, Cesur
  • Keskin, Mustafa
  • Yalçın, Orhan

Abstract

We investigate the temperature dependence of the order parameters of the Blume–Capel model for zero magnetic field in the lowest approximation of the cluster variation method which is identical to the mean-field approximation. Besides the stable branches of the order parameters, we establish the metastable and unstable parts of these curves for the various values of the coupling parameter, α=D/J. We also study the dynamics of the model by the path probability method, since the metastable behavior is a dynamical behavior. From this study, the “flatness” property of metastable states, “overshooting” phenomenon and as well as the role of the unstable state are seen explicitly. On the other hand, we also investigate how to obtain the metastable phases with two long-range order parameters. Finally, we calculate the phase transitions of the metastable and unstable branches of order parameters besides the stable branches and present the complete phase diagram.

Suggested Citation

  • Ekiz, Cesur & Keskin, Mustafa & Yalçın, Orhan, 2001. "Metastable and unstable states of the Blume–Capel model obtained by the cluster variation method and the path probability method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 215-232.
    • Handle: RePEc:eee:phsmap:v:293:y:2001:i:1:p:215-232
    DOI: 10.1016/S0378-4371(00)00595-1
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    Cited by:

    1. Ozer, Mahmut, 2005. "Determination of rate kinetics in ion channels by the path probability method and Onsager reciprocity theorem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(3), pages 397-414.
    2. Mendes, R.G.B. & Sá Barreto, F.C. & Santos, J.P., 2018. "Thermodynamic states of the mixed spin 1/2 and spin 1 hexagonal nanotube system obtained from a eighteen-site cluster within an improved mean field approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1186-1195.
    3. 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.

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