  In this work we compare numerically exact Quantum Monte Carlo (QMC)
calculations and Green function theory (GFT) calculations of thin ferromagnetic
films including second order anisotropies. Thereby we concentrate on easy plane
systems, i.e. systems for which the anisotropy favors a magnetization parallel
to the film plane. We discuss these systems in perpendicular external field,
i.e. B parallel to the film normal. GFT results are in good agreement with QMC
for high enough fields and temperatures. Below a critical field or a critical
temperature no collinear stable magnetization exists in GFT. On the other hand
QMC gives finite magnetization even below those critical values. This indicates
that there occurs a transition from non-collinear to collinear configurations
with increasing field or temperature. For slightly tilted external fields a
rotation of magnetization from out-of-plane to in-plane orientation is found
with decreasing temperature.
