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.
Keywords:
Tsallis statistics, Ising model, Magnetization,
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- 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.
- Başlangıç: 2018
- Yayıncı: Uşak Üniversitesi