Phase diagrams of spin-3/2 Ising model in the presence of random crystal field within the effective field theory based on two approximations

The bimodal random crystal field (Δ) effects are investigated on the phase diagrams of spin-3/2 Ising model by using the effective-field theory with correlations based on two approximations: the general van der Waerden identity and the approximated van der Waerden identity. In our approach, the crystal field is either turned on or turned off randomly for a given probability p or q=1-p, respectively. Then the phase diagrams are constructed on the (Δ, kT/J) and (p, kT/J) planes for given p and Δ, respectively, when the coordination number is z=3. Furthermore, the effect of randomization of the crystal field is illustrated on the (Δ, kT/J) plane for p=0.5 when z=3, 4, and 6. All these are carried out for both approximations and then the results are compared to point out the differences. In addition to the lines of second-order phase transitions, the model also exhibits first-order phase transitions and the lines of which terminate at the isolated critical points for high p values.