  We introduce a Heisenberg Hamiltonian for describing the magnetic properties
of GaMnAs. Electronic degrees of freedom are integrated out leading to a
pairwise interaction between Mn spins. Monte Carlo simulations in large systems
are then possible, and reliable values for the Curie temperatures of diluted
magnetic semiconductors can be obtained. Comparison of mean field and Monte
Carlo Curie temperatures shows that fluctuation effects are important for
systems with a large hole density and/or increasing locality in the carriers-Mn
coupling. We have also compared the results obtained by using a realistic ${\bf
k} \cdot {\bf p}$ model with those of a simplified parabolic two band model. In
the two band model, the existence of a spherical Fermi surface produces the
expected sign oscillations in the coupling between Mn spins, magnifying the
effect of fluctuations and leading to the eventual disappearance of
ferromagnetism . In the more realistic ${\bf k} \cdot {\bf p}$ model, warping
of the Fermi surface diminishes the sign oscillations in the effective coupling
and, therefore, the effect of fluctuations on the critical temperature is
severely reduced. Finally, by studying the collective magnetic excitations of
the this model at zero temperature, we analyze the stability of the fully
polarized ferromagnetic ground state.
