The site diluted transverse spin-1 Ising model with a longitudinal crystal-field

The site diluted transverse spin-1 Ising model with a longitudinal crystal field on a square lattice is investigated within the effective field theory with a probability distribution technique that accounts for the single-site kinematic relations. The temperature dependence of the longitudinal and transverse magnetizations and quadrupolar moments is presented for selected values of the site dilution c and the strengths of the transverse field Ω/J and the longitudinal crystal field D/J. Results for the concentration dependence of the transition temperature are given. In a certain range of negative values of the strength of the crystal field D/J when it becomes sufficiently negative, we found re-entrant phenomenon which disappears with increasing the value of the strength of the transverse field.