The Critical Properties And Magnetizations Of Random Transverse Uniaxial And Biaxial Crystal Field Ising Model

Within the framework of the effective field theory (EFT) and cutting approximation, critical properties of spin-1 transverse random crystal field Ising model and biaxial Ising model with both longitudinal crystal field and transverse crystal field are investigated.Firstly, we study the phase diagrams and magnetization behaviors of transverse random crystal field Ising model for square lattice and simple cubic lattice respectively. We discuss in detail the influence of transverse random crystal field concentration and crystal field ratio on the phase diagrams and magnetization behaviors. We give phase diagrams in T - Dx space and magnetization curves in m - T space. Under crystal field dilution condition, there exists the peak value of critical temperature in the direction of negative crystal field and reentrant phenomena in the direction positive critical field. While choosing crystal field ratioα=+0.5 andα=-0.5, the range of magnetic ordered phase shrinks. In particular, we find that, with decreasing of concentration, the peak value of critical temperature undergoes a crossover from negative to positive direction of transverse crystal field when the ratioα=-0.5. The magnetization behaviors have apparent differences for a given negative crystal field value when the crystal field ratio is different. The magnetizations have a lot of differences at high and low temperatures.Secondly, critical properties of biaxial Ising model with both longitudinal crystal field and transverse crystal field are investigated for a simple cubic lattice. When transverse crystal field is diluted, the tricritical point (TCP) and its trajectory are discussed in T - Dx and T - Dz space. A new phenomenon of two TCPs is found in T - Dx space. There exists a second-order line between two first-order lines, separated by two TCPs. The change of dilution concentration leads to a complex relation of trajectory of the TCP. The degenerate patterns at ground state appear by changing longitudinal crystal field. The range of ordered phase for transition lines labeled positive or (negative) value of Dx / J becomes larger or (smaller) with the decrease of t x in T - Dz space. When longitudinal crystal field and transverse crystal field are diluted simultaneously in T - Dz space, we reduce the dilution concentration of transverse crystal field and find that the dilution concentration range of longitudinal crystal field to maintain TCP's existence is decreased. In this case, the system shows different behaviors while choosing positive or negative transverse crystal field. When transverse crystal field is positive, double TCPs appear in certain dilution concentration range of longitudinal crystal field. However, there exists only one TCP when transverse crystal field is negative.