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The phase diagram of the spin-1 Ising model in the presence of a biaxialcrystal-field anisotropy is studied within the framework of a variationalapproach, based on the Bogolyubov inequality for the free energy. We haveinvestigated the effects of a transverse crystal-field $D_{y}$ on the phasediagram in the $T-D_{x}$ plane. Results obtained by using effective-fieldtheory (EFT) on the honeycomb (% $z=3$), square ($z=4$) and simple cubic($z=6$) lattices ($z$ is the coordination number) show only continuous phasetransitions, while the variational approach presents first-order and continuousphase transitions for $D_{y}=0$% . We have also used the EFT for larger valuesof $z$ and we observe the presence of tricritical points in the phase diagrams,for $z\geq 7$, in accordance with the variational approach results.

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