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A SPIN-1 ISING MODEL INVESTIGATION OF THE MAGNETIC SYSTEM IS CARRIED OUT WITHIN THE CONTEXT OF GENERALIZED STATISTICAL MECHANICS

Year 2023, Volume: 6 Issue: 2, 67 - 73, 29.12.2023
https://doi.org/10.47137/uujes.1300516

Abstract

In this study magnetization has been investigated with the help of Ising model in the frame of non-extensive statistical mechanics where a behavior of interacting elementary moments ensemble is taken into consideration. To examine the physical systems with three states and two order parameters, researchers employ the spin-1 single lattice Ising model or three-state systems. Within this model, various thermodynamic characteristics of phenomena like ferromagnetism in binary alloys, liquid mixtures, liquid-crystal mixtures, freezing, magnetic order, phase transformations, semi-stable and unstable states, ordered and disordered transitions have been investigated for three distinct forms associated with q < 1, q = 1, and q > 1. In this context, q represents the non-extensivity parameter of Tsallis statistics.

References

  • Yeomans JM. Statistical Mechanics of Phase Transition, Clerandon Press, 1992.
  • Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys., 1998; 52:479-487.,
  • Ising EZ. Contribution to the Theory of Ferromagnetism. Z. Physics, 1925; 31:253-258.
  • Landau L. The Movement of Electrons in the Crystal Lattice. Z. Phys. Sowjet Union, 1933; 4: 644-645.
  • Cabren B. Magnéto-chimie. J. Chim. Phys., 1918; 16: 442-501.
  • Bak P and Boehm JV. Ising Model with Solitons, Phasons, and "The Devil's Staircase", Phy. Rev. 1980; B21: 5297-5308.
  • Binder K and Young AP. Spin Glasses: Experimental Facts, Theoretical Concepts, and Open Questions, Rev. Mod. Phys., 1986; 58: 801-976.
  • Binek C and Kleemann W. Domainlike antiferromagnetic correlations of paramagnetic FeCl2: A field-induced Griffiths phase?, Phys. Rev. Lett. 1994; 72: 1287-1290.
  • Tsallis C, Mendes RS, Plastino AR. The role of constraints within generalized nonextensive statistics, Physica A. 1998; 261: 534-554.
  • Tsallis C. Possible Generalization of Boltzmann-Gibbs Statistics, Journal of Statistical Physics. 1988; 52: 479487.
  • Tsallis C. Nonextensive Statistical Mechanics and Nonlinear Dynamics, Physica D. 2004; 193: 153-193.
  • Tarasov VE. Possible Experimental Test of Continuous Medium Model for Fractal Media, Physics Letters A. 2005; 336 467-472.
  • Tsallis C. Entropic Nonextensivity: A Possible Measure of Complexity, Chaos, Solitions and Fractals. 2002; 13: 371-391.
  • Kaneyoshi T. A New Type of Cluster Theory in Ising Models (I), Physica A. 1999; 269: 344-356.
  • Tsallis C, Borges EP. Comment on “Pricing of Financial Derivatives Based on The Tsallis Statistical Theory” by Zhao, Pan, Yue and Zhang, Chaos, Solitons and Fractals. 2021; 148: 111025-111026.
Year 2023, Volume: 6 Issue: 2, 67 - 73, 29.12.2023
https://doi.org/10.47137/uujes.1300516

Abstract

References

  • Yeomans JM. Statistical Mechanics of Phase Transition, Clerandon Press, 1992.
  • Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys., 1998; 52:479-487.,
  • Ising EZ. Contribution to the Theory of Ferromagnetism. Z. Physics, 1925; 31:253-258.
  • Landau L. The Movement of Electrons in the Crystal Lattice. Z. Phys. Sowjet Union, 1933; 4: 644-645.
  • Cabren B. Magnéto-chimie. J. Chim. Phys., 1918; 16: 442-501.
  • Bak P and Boehm JV. Ising Model with Solitons, Phasons, and "The Devil's Staircase", Phy. Rev. 1980; B21: 5297-5308.
  • Binder K and Young AP. Spin Glasses: Experimental Facts, Theoretical Concepts, and Open Questions, Rev. Mod. Phys., 1986; 58: 801-976.
  • Binek C and Kleemann W. Domainlike antiferromagnetic correlations of paramagnetic FeCl2: A field-induced Griffiths phase?, Phys. Rev. Lett. 1994; 72: 1287-1290.
  • Tsallis C, Mendes RS, Plastino AR. The role of constraints within generalized nonextensive statistics, Physica A. 1998; 261: 534-554.
  • Tsallis C. Possible Generalization of Boltzmann-Gibbs Statistics, Journal of Statistical Physics. 1988; 52: 479487.
  • Tsallis C. Nonextensive Statistical Mechanics and Nonlinear Dynamics, Physica D. 2004; 193: 153-193.
  • Tarasov VE. Possible Experimental Test of Continuous Medium Model for Fractal Media, Physics Letters A. 2005; 336 467-472.
  • Tsallis C. Entropic Nonextensivity: A Possible Measure of Complexity, Chaos, Solitions and Fractals. 2002; 13: 371-391.
  • Kaneyoshi T. A New Type of Cluster Theory in Ising Models (I), Physica A. 1999; 269: 344-356.
  • Tsallis C, Borges EP. Comment on “Pricing of Financial Derivatives Based on The Tsallis Statistical Theory” by Zhao, Pan, Yue and Zhang, Chaos, Solitons and Fractals. 2021; 148: 111025-111026.
There are 15 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ozan Kıyıkcı 0000-0002-9024-8194

Kadriye Kaçmaz 0000-0002-2998-3341

Musab Tuğrul 0000-0003-1926-5159

Görkem Oylumluoğlu 0000-0002-7398-4018

Publication Date December 29, 2023
Submission Date May 22, 2023
Acceptance Date October 16, 2023
Published in Issue Year 2023 Volume: 6 Issue: 2

Cite

APA Kıyıkcı, O., Kaçmaz, K., Tuğrul, M., Oylumluoğlu, G. (2023). A SPIN-1 ISING MODEL INVESTIGATION OF THE MAGNETIC SYSTEM IS CARRIED OUT WITHIN THE CONTEXT OF GENERALIZED STATISTICAL MECHANICS. Usak University Journal of Engineering Sciences, 6(2), 67-73. https://doi.org/10.47137/uujes.1300516
AMA Kıyıkcı O, Kaçmaz K, Tuğrul M, Oylumluoğlu G. A SPIN-1 ISING MODEL INVESTIGATION OF THE MAGNETIC SYSTEM IS CARRIED OUT WITHIN THE CONTEXT OF GENERALIZED STATISTICAL MECHANICS. UUJES. December 2023;6(2):67-73. doi:10.47137/uujes.1300516
Chicago Kıyıkcı, Ozan, Kadriye Kaçmaz, Musab Tuğrul, and Görkem Oylumluoğlu. “A SPIN-1 ISING MODEL INVESTIGATION OF THE MAGNETIC SYSTEM IS CARRIED OUT WITHIN THE CONTEXT OF GENERALIZED STATISTICAL MECHANICS”. Usak University Journal of Engineering Sciences 6, no. 2 (December 2023): 67-73. https://doi.org/10.47137/uujes.1300516.
EndNote Kıyıkcı O, Kaçmaz K, Tuğrul M, Oylumluoğlu G (December 1, 2023) A SPIN-1 ISING MODEL INVESTIGATION OF THE MAGNETIC SYSTEM IS CARRIED OUT WITHIN THE CONTEXT OF GENERALIZED STATISTICAL MECHANICS. Usak University Journal of Engineering Sciences 6 2 67–73.
IEEE O. Kıyıkcı, K. Kaçmaz, M. Tuğrul, and G. Oylumluoğlu, “A SPIN-1 ISING MODEL INVESTIGATION OF THE MAGNETIC SYSTEM IS CARRIED OUT WITHIN THE CONTEXT OF GENERALIZED STATISTICAL MECHANICS”, UUJES, vol. 6, no. 2, pp. 67–73, 2023, doi: 10.47137/uujes.1300516.
ISNAD Kıyıkcı, Ozan et al. “A SPIN-1 ISING MODEL INVESTIGATION OF THE MAGNETIC SYSTEM IS CARRIED OUT WITHIN THE CONTEXT OF GENERALIZED STATISTICAL MECHANICS”. Usak University Journal of Engineering Sciences 6/2 (December 2023), 67-73. https://doi.org/10.47137/uujes.1300516.
JAMA Kıyıkcı O, Kaçmaz K, Tuğrul M, Oylumluoğlu G. A SPIN-1 ISING MODEL INVESTIGATION OF THE MAGNETIC SYSTEM IS CARRIED OUT WITHIN THE CONTEXT OF GENERALIZED STATISTICAL MECHANICS. UUJES. 2023;6:67–73.
MLA Kıyıkcı, Ozan et al. “A SPIN-1 ISING MODEL INVESTIGATION OF THE MAGNETIC SYSTEM IS CARRIED OUT WITHIN THE CONTEXT OF GENERALIZED STATISTICAL MECHANICS”. Usak University Journal of Engineering Sciences, vol. 6, no. 2, 2023, pp. 67-73, doi:10.47137/uujes.1300516.
Vancouver Kıyıkcı O, Kaçmaz K, Tuğrul M, Oylumluoğlu G. A SPIN-1 ISING MODEL INVESTIGATION OF THE MAGNETIC SYSTEM IS CARRIED OUT WITHIN THE CONTEXT OF GENERALIZED STATISTICAL MECHANICS. UUJES. 2023;6(2):67-73.

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