Investigation of the critical behavior of the spin - 2 antiferromagnetic ising model on bethe lattice in the presence of the random crystal field

In this thesis, phase diagrams of spin-2 Antiferromagnetic Ising model on Bethe lattice are investigated in the presence of random crystal field using exact recursion relations. First of all, the magnetization order parameters equations necessary to investigate the critical properties of the model were obtained in terms of exact recursion relations in the presence of a random crystal field. The solutions of these equations were obtained by using the iteration method by means of a suitable programming language. Then, the differences of thermal behavior of the layout parameters of the model from the pure state were investigated. First-order and second-order phase transition temperatures occurring in the model were determined for coordination number q= 4. Then, phase diagrams of the model were obtained for coordination number q= 4 and random crystal field values with different probability values in the (H, T) plane. The model exhibits points such as the tri critical point (T), critical endpoint (E), and critical point (C), which receive special names according to the various convergence and termination critical points of first-order and second-order phase transition lines. In addition, reentrant behavior was observed in the second-order phase transition lines for some probability values. As a result, it is explained how the random crystal field affects the critical behaviors occurring in the model.