The Study Of Thermodynamic Behavior And Phase Transitions Of The Mixed Spin System On Cayley Tree

Using the recursion method, the phase transition and the thermodynamic behavior of the mixed spin-1/2 and spin-3/2 Ising system on the two-fold Cayley tree are studied for the ferromagnetic and ferrimagnetic cases, respectively. The main results of this thesis are given as follows:For the ferromagnetic case, the effects of the crystal-field interaction and the coordination number on the thermodynamic behavior of the mixed spin system are investigated. The sublattice magnetizations M_A and M_B as functions of temperature and the phase diagrams of the system are obtained by the numerical calculation. The results show that for the same coordination number, the behavior of M_A is different for different values of the crystal-field interaction, while the behavior of M_B is similar. When the value of the crystal-field interaction is certain, the transition temperature T_c becomes larger as the coordination number q increases. On the other hand, T_c decreases to an invariable value T_o when the crystal-field interaction becomes large enough. It is also shown that there is no tricritical behavior for ferromagnetic system.For the ferrimagnetic case, the relations of sublattice magnetizations M_A M_B and the total magnetization M with the temperature are obtained, respectively. It is found that the behavior of M is similar to that of M_A. The behavior of M_B is agree with that of the ferromagnetic case, but the behavior of |M_A| is consistent with the behavior of M_A in the ferromagnetic case. There is also no tricritical behavior for the ferrimagnetic system.