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

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.

Keywords

• Tsallis statistics
• Ising model
• Magnetization

References

1. Yeomans JM. Statistical Mechanics of Phase Transition, Clerandon Press, 1992.
2. Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys., 1998; 52:479-487.,
3. Ising EZ. Contribution to the Theory of Ferromagnetism. Z. Physics, 1925; 31:253-258.
4. Landau L. The Movement of Electrons in the Crystal Lattice. Z. Phys. Sowjet Union, 1933; 4: 644-645.
5. Cabren B. Magnéto-chimie. J. Chim. Phys., 1918; 16: 442-501.
6. Bak P and Boehm JV. Ising Model with Solitons, Phasons, and "The Devil's Staircase", Phy. Rev. 1980; B21: 5297-5308.
7. Binder K and Young AP. Spin Glasses: Experimental Facts, Theoretical Concepts, and Open Questions, Rev. Mod. Phys., 1986; 58: 801-976.
8. Binek C and Kleemann W. Domainlike antiferromagnetic correlations of paramagnetic FeCl2: A field-induced Griffiths phase?, Phys. Rev. Lett. 1994; 72: 1287-1290.

9. Tsallis C, Mendes RS, Plastino AR. The role of constraints within generalized nonextensive statistics, Physica A. 1998; 261: 534-554.
10. Tsallis C. Possible Generalization of Boltzmann-Gibbs Statistics, Journal of Statistical Physics. 1988; 52: 479487.
11. Tsallis C. Nonextensive Statistical Mechanics and Nonlinear Dynamics, Physica D. 2004; 193: 153-193.
12. Tarasov VE. Possible Experimental Test of Continuous Medium Model for Fractal Media, Physics Letters A. 2005; 336 467-472.
13. Tsallis C. Entropic Nonextensivity: A Possible Measure of Complexity, Chaos, Solitions and Fractals. 2002; 13: 371-391.
14. Kaneyoshi T. A New Type of Cluster Theory in Ising Models (I), Physica A. 1999; 269: 344-356.
15. 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.