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Generalization of the mean-field Ising model within Tsallis thermostatistics

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  • Büyükkiliç, Fevzi
  • Demirhan, Doǧan
  • Tirnakli, Uǧur

Abstract

In this study, the mean-field Ising model, using the Bogolyubov inequality which has been obtained in the framework of the generalized statistical thermodynamics (GST), suitable for non-extensive systems, has been investigated. Generalized expressions for the mean-field magnetization and free energy have been established. These new results have been verified by the fact that they transform to the well-known Boltzmann-Gibbs results in the q → 1 limiting case. For the index q which characterizes the fractal structure of the magnetic system, an interval has been established where the generalized mean-field free energy has a minimum and mean-field magnetization has a corresponding finite value. The interval of q is consistent with paramagnetic free spin systems.

Suggested Citation

  • Büyükkiliç, Fevzi & Demirhan, Doǧan & Tirnakli, Uǧur, 1997. "Generalization of the mean-field Ising model within Tsallis thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 238(1), pages 285-294.
    • Handle: RePEc:eee:phsmap:v:238:y:1997:i:1:p:285-294
    DOI: 10.1016/S0378-4371(96)00440-2
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