TY - JOUR T1 - A SPIN-1 ISING MODEL INVESTIGATION OF THE MAGNETIC SYSTEM IS CARRIED OUT WITHIN THE CONTEXT OF GENERALIZED STATISTICAL MECHANICS AU - Oylumluoğlu, Görkem AU - Kıyıkcı, Ozan AU - Kaçmaz, Kadriye AU - Tuğrul, Musab PY - 2023 DA - December Y2 - 2023 DO - 10.47137/uujes.1300516 JF - Usak University Journal of Engineering Sciences JO - UUJES PB - Usak University WT - DergiPark SN - 2651-3447 SP - 67 EP - 73 VL - 6 IS - 2 LA - en AB - 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. KW - Tsallis statistics KW - Ising model KW - Magnetization CR - Yeomans JM. Statistical Mechanics of Phase Transition, Clerandon Press, 1992. CR - Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys., 1998; 52:479-487., CR - Ising EZ. Contribution to the Theory of Ferromagnetism. Z. Physics, 1925; 31:253-258. CR - Landau L. The Movement of Electrons in the Crystal Lattice. Z. Phys. Sowjet Union, 1933; 4: 644-645. CR - Cabren B. Magnéto-chimie. J. Chim. Phys., 1918; 16: 442-501. CR - Bak P and Boehm JV. Ising Model with Solitons, Phasons, and "The Devil's Staircase", Phy. Rev. 1980; B21: 5297-5308. CR - Binder K and Young AP. Spin Glasses: Experimental Facts, Theoretical Concepts, and Open Questions, Rev. Mod. Phys., 1986; 58: 801-976. CR - Binek C and Kleemann W. Domainlike antiferromagnetic correlations of paramagnetic FeCl2: A field-induced Griffiths phase?, Phys. Rev. Lett. 1994; 72: 1287-1290. CR - Tsallis C, Mendes RS, Plastino AR. The role of constraints within generalized nonextensive statistics, Physica A. 1998; 261: 534-554. CR - Tsallis C. Possible Generalization of Boltzmann-Gibbs Statistics, Journal of Statistical Physics. 1988; 52: 479487. CR - Tsallis C. Nonextensive Statistical Mechanics and Nonlinear Dynamics, Physica D. 2004; 193: 153-193. CR - Tarasov VE. Possible Experimental Test of Continuous Medium Model for Fractal Media, Physics Letters A. 2005; 336 467-472. CR - Tsallis C. Entropic Nonextensivity: A Possible Measure of Complexity, Chaos, Solitions and Fractals. 2002; 13: 371-391. CR - Kaneyoshi T. A New Type of Cluster Theory in Ising Models (I), Physica A. 1999; 269: 344-356. CR - 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. UR - https://doi.org/10.47137/uujes.1300516 L1 - https://dergipark.org.tr/en/download/article-file/3157377 ER -