Obtaining the phase diagrams of mixed spin-1 and spin-2 Blume-Emery-Griffiths model on Bethe Lattice

This thesis presents for the first time a comprehensive study of the critical behavior of the mixed spin-1 and spin-2 Blume-Emery-Griffiths (BEG) model on the Bethe lattice. The model is studied theoretically on the Bethe lattice using the method of exact recursion relations. The mixed-spin BEG model provides an ideal theoretical model for understanding molecular-based magnetic materials and their applications found in various technological tools, such as thermomagnetic recording systems. Expressions of the model's sublattice magnetizations and quadrupole moments were obtained in terms of full recursion relations. These equations were solved using a numerical method, the iteration method, in a suitable computer programming language. A comprehensive investigation of the thermal variations of these order parameters of the system in the absence and presence of the crystal field interaction parameter D was carried out. This includes a detailed analysis of the phase transitions occurring in the system, whether they are first-order, second-order, or higher-order. Phase diagrams of the mixed spin-1 and spin-2 isotropic BEG model in the absence of a crystal field parameter and phase diagrams of the mixed spin-1 and spin-2 BEG model in the presence of various crystal field parameters were obtained in detail in the (K, T) plane for coordination numbers q=3, 4, and 6. One ordered ferrimagnetic phase, one ordered antiferromagnetic phase, and one disordered paramagnetic phase were detected in the model. In the isotropic case, for coordination number q=3, only second-order phase transition lines form the boundary between the region of ordered ferrimagnetic phases and the region of disordered paramagnetic phases, while for q=4 and q=6, both second-order and first-order phase transition lines form boundaries together. In the non-isotropic case, both second-order and first-order phase transition lines form boundaries between the ordered phase region and the disordered phase region for all coordination numbers. In both cases, three critical points exist. In the non-isotropic case, the first-order phase transition lines exhibit reentrant behavior. The study also investigated in detail the compensation temperature, which is the critical temperature below the Curie temperature at which the net metamorphosis is zero. In both cases, no compensation temperature point was found.