Variational-method study of the spin-1 Ising model with biaxial crystal-field anisotropy

The phase diagram of the spin-1 Ising model in the presence of a biaxial crystal-field anisotropy is studied within the framework of a variational approach, based on the Bogolyubov inequality for the free energy. We have investigated the effects of a transverse crystal field D-y on the phase diagram in the T-D-x plane. Results obtained by using effective-field theory (EFT) on the honeycomb (z=3), square (z=4), and simple cubic (z=6) lattices (z is the coordination number) show only continuous phase transitions, while the variational approach presents first-order and continuous phase transitions for D-y=0. We have also used the EFT for larger values of z and we observe the presence of tricritical points in the phase diagrams, for z >= 7, in accordance with the variational approach results.