  Using a recently developed semi-analytical method (Self-Consistent Local RPA
or SC-LRPA) we study the stability of the ferromagnetic phase in diluted
magnetic systems where the exchange coupling between magnetic impurities are of
RKKY form. A short discussion of the relevance of these calculations with
respect to the ferromagnetism observed in diluted ferromagnetic materials is
provided. Then, within a two step approach, we study ferromagnetism in
$Zn_{1-x}Cr_{x}Te$. In the first step of our study, we calculate the magnetic
couplings between Mn impurities within the LDA. In the second step, we
diagonalize the resulting effective Heisenberg Hamiltonian using the SC-LRPA.
We also compare, when available, our calculations with Monte Carlo simulations
and experimental measurements.
