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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
https://izlik.org/JA87BR74JW

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
https://izlik.org/JA87BR74JW

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 Research Article
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

Submission Date May 22, 2023
Acceptance Date October 16, 2023
Publication Date December 29, 2023
DOI https://doi.org/10.47137/uujes.1300516
IZ https://izlik.org/JA87BR74JW
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 1.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. doi:10.47137/uujes.1300516
Chicago Kıyıkcı, Ozan, Kadriye Kaçmaz, Musab Tuğrul, and Görkem Oylumluoğlu. 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.
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 [1]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, Dec. 2023, doi: 10.47137/uujes.1300516.
ISNAD Kıyıkcı, Ozan - Kaçmaz, Kadriye - Tuğrul, Musab - Oylumluoğlu, Görkem. “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 1, 2023): 67-73. https://doi.org/10.47137/uujes.1300516.
JAMA 1.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, Dec. 2023, pp. 67-73, doi:10.47137/uujes.1300516.
Vancouver 1.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 [Internet]. 2023 Dec. 1;6(2):67-73. Available from: https://izlik.org/JA87BR74JW

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