  The strength of perpendicular anisotropy is known to drive the spin
reorientation in thin magnetic films. Here we consider the effect different
order anisotropies have on two phase transitions; the spin reorientation
transition and the orientational order transition. We find that the relative
magnitude of different order anisotropies can significantly enhance or suppress
the degree to which the system reorients. Specifically Monte Carlo simulations
reveal significant changes in the cone angle and planar magnetization. In order
to facilitate rapid computation we have developed a stream processing
technique, suitable for use on GPU systems, for computing the transition
probabilities in two dimensional systems with dipole interactions.
