Critical behaviors of mixed spin-1/2 and spin-2 Blume-Emery-Griffiths model on the bethe lattice

In this thesis, the critical behaviors of the mixed spin-1/2 and spin-2 Blume-Emer-Griffiths ferrimagnetic Ising model, which can be used as a model in the study of different properties of molecularly structured magnetic materials, is investigated theoretically on the Bethe lattice using the exact recurrence relations method. The expressions for the sublattice dipole and quadrupole magnetizations of the model are obtained in terms of the exact recurrence relations. These equations were solved numerically using the iteration method in a suitable computer programming language. In order to determine the nature of the phase transformations occurring in the model, the temperature variation behavior of the sublattice dipole and quadrupole magnetizations was investigated for various values of biquadratic exchange (K) interactions and crystal field (D) parameters. Phase diagrams of the model were then obtained in the (K, T) plane for different coordination numbers q = 3, 4, and 6 for various values of the crystal field, both positive and negative. However, mixed-spin models also exhibit a new type of critical temperature, called the compensation temperature, where the net magnetization of the system is zero below the phase transition temperature. The existence of this compensation temperature provides important possibilities for the design of technological devices. The compensation temperatures occurring in the model have been extensively investigated and shown in phase diagrams for various values of crystal field. It was also found that the model exhibits three different types of phase diagrams, according to the value of the coordination number. In the first type of phase diagrams, there are only second-order phase transition lines separating the ordered and disordered phases; in the second type of phase diagrams, in addition to the second-order phase transition lines, there are also compensation temperature lines; and in the third type of phase diagrams, there are both second- and first-order phase transition lines separating the phases in question and compensation temperature lines. Finally, for coordination number q = 6, a special critical point, the tricritical points, where the second-order phase transformation temperature lines end and the first-order phase transition temperature lines begin, and isolated end points where the first-order phase transition temperatures end are also obtained in the phase diagrams of the model.