  Carrier induced ferromagnetism in diluted III-V semi-conductor is analyzed
within a two step approach. First, within a single site CPA formalism, we
calculate the element resolved averaged Green's function of the itinerant
carrier. Then using a generalized RKKY formula we evaluate the Mn-Mn long-range
exchange integrals and the Curie temperature as a function of the exchange
parameter, magnetic impurity concentration and carrier density. The effect of
the disorder (impurity scattering) appears to play a crucial role. The standard
RKKY calculation (no scattering processes), strongly underestimate the Curie
temperature and is inappropriate to describe magnetism in diluted magnetic
semi-conductors. It is also shown that an antiferromagnetic exchange favors
higher Curie temperature.
