The properties of Mn-doped GaAs are studied at several doping levels and hole
compensations, using a real-space Hamiltonian on an fcc lattice that reproduces
the valence bands of undoped GaAs. Large-scale Monte Carlo (MC) simulations on
a Cray XT3 supercomputer, using up to a thousand nodes, were needed to make
this effort possible. Our analysis considers both the spin-orbit interaction
and the random distribution of the Mn ions. The hopping amplitudes are
functions of the GaAs Luttinger parameters. At the coupling J~1.2eV deduced
from photoemission experiments, the MC Curie temperature and the shape of the
magnetization curves are in agreement with experimental results for annealed
samples. Although there are sizable differences with mean-field predictions,
the system is found to be closer to a hole-fluid regime than to localized
carriers