The phase diagrams of mixed spin-1/2 and spin-7/2 Blume-Emery-Griffiths model on the bethe lattice

The critical behaviors of the mixed spin-1/2 and spin-7/2 Blume-Emery-Griffiths (BEG) model on the Bethe lattice are fully studied in this thesis, which is an area that has not been looked into before. The model was theoretically investigated on the Bethe lattice using the exact recursion relations method. For better understanding of molecular-based magnetic materials and their uses in many technological devices, like thermomagnetic recording systems, the mixed-spin BEG model is a great starting point. Expressions for the sublattice dipole moments and quadrupole moments were obtained in terms of exact recursion relations. These equations were solved using an iteration method in an appropriate computer programming language. A thorough investigation was conducted into the thermal variations of these order parameters in the presence and absence of the biquadratic interaction parameter K. This includes a detailed analysis of the phase transitions occurring in the system, determining whether they are first-order, second-order, or of higher order. Additionally, this study presents an extensive mapping of the model's phase diagrams on the (D, T) plane for coordination numbers q=3, 4, and 6 and for various positive, zero, and various negative values of the biquadratic interaction parameter. Three distinct ordered ferrimagnetic phases, one ordered antiferromagnetic phase, three different hybrid phases, and one disordered paramagnetic phase were detected in the model. For coordination numbers q=3, 4, and 6, it was found that the ordered phases and the disordered paramagnetic phase are separated only by second-order phase transition lines. Furthermore, the study aims to reveal the compensation temperature, a critical temperature below the Curie temperature where the net magnetization is zero, by extensively investigating the temperature variations of the sublattice net magnetization curves over a wide range of system parameters.