  Magnetic properties of Mn-doped GaAs are re-investigated within a realistic
multiband description of the host valence bands. We explicitely demonstrate
that the recent Monte Carlo (MC) simulations performed on a large scale
supercomputer suffer from severe shortcomings. Indeed, it is shown, using
identical parameters that (i) the calculated Zeeman-splitting largely
underestimates that obtained from first principle studies, (ii) the couplings
exhibit strong RKKY oscillations, (iii) the stability region for ferromagnetism
is much narrower than obtained previously and (iv) the calculated Curie
temperatures appear to be at least one order of magnitudes smaller. We show
that the proposed choice of physical parameters cannot describe the physics in
(Ga,Mn)As.
