Bethe kafes üzerinde karma spin-1 ve spin-3/2 Blume-Emery-Griffiths modeli

In this thesis,the critical behavior of the mixed spin-1 and spin-3/2 Blume-Emerry￾Griffiths ferrimagnetic Ising model, which can be used as a model, was investigated theoretically on the Bethe lattice using the method of exact recurrence relations in the study of different properties of molecularly structured magnetic materials. The expressions for the sublattice dipole moments and quadrupole moments of the model are obtained in terms of the full recurrence relations. By using the numerical iteration method, a suitable computer programming language was able to solve these equations. In order to determine the types of phase transitions occurring in the model, the change behaviors of the sublattice dipole moments and quadrupole moments with temperature was investigated. Phase diagrams of the mixed spin-1 and spin-3/2 isotropic BEG model in the absence of a crystal field parameter and phase diagrams of the mixed spin-1 and spin-3/2 BEG model in the presence of a negative-valued crystal field parameter are obtained in detail in the (K,T) plane for coordination numbers q = 3, 4, and 6. However, mixed-spin models also exhibit a new type of critical temperature, called the compensation temperature, where the net dipole moment of the system reaches 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 were thoroughly investigated and shown in phase diagrams. For coordination numbers q = 3, 4, and 6, both the mixed spin-1 and spin-3/2 isotropic BEG model and the mixed spin-1 and spin-3/2 BEG model in the presence of a negative-valued crystal field exhibit compensation temperature lines and both second-order phase transition lines and first-order phase transition lines separating the ordered ferrimagnetic phase regions from the disordered paramagnetic phase region. In both cases of the model, there is a special critical point, the tri critical points (o), where the second-order phase transition temperature lines end and the first￾order phase transition temperature lines begin. In addition, in the mixed spin-1 and spin￾3/2 BEG model in the presence of a negative-valued crystal field, there are critical isolated points () where the first-order phase transition temperature lines end and a -order phase transition temperature line and the compensation temperature line meet. Finally, for favorable system parameters, one compensation temperature point appears in the mixed spin-1 and spin-3/2 isotropic BEG model, while two compensation temperature points appear in the mixed spin-1 and spin￾3/2 BEG model in the presence of a negative-valued crystal field.