We discuss finite temperature fluctuations of the magnetization ill in
ultrathin magnetic films where spins interact with short-range exchan
ge (J), anisotropy (K) and long-range dipolar (g) couplings. Phase bou
ndaries for a triangular lattice are obtained from Monte Carlo simulat
ions as a function of J, g and K. For nonzero g, the magnetization can
rotate from the z to the in-plane direction. The transition temperatu
re as a function of the effective anisotropy field K-g/0.1208 is essen
tially unchanged as g becomes zero. This suggests a new physical pictu
re in which, as the temperature is increased, the change in the direct
ion of M for g not equal 0 is closely connected with the Ising transit
ion for g = 0 when the M(2), disappears. Mean field calculations sugge
st three transitions where only M(z) is finite at low temperature. As
the temperature is increased, (1) M(x) becomes nonzero, (2) M(z) becom
es zero and eventually (3) M(x) becomes zero.