Magnetism in (III, Mn)-V Diluted Magnetic Semiconductors: Effective   Heisenberg Model
  The magnetic properties of the diluted magnetic semiconductors (DMS) (Ga, Mn)As and (Ga, Mn)N are investigated by means of an effective Heisenberg model, whose exchange parameters are obtained from first-principle calculations. The finite-temperature properties of the model are studied numerically using a method based upon the Tyablikov approximation. The method properly incorporates the effects of positional disorder present in DMS. The resulting Curie temperatures for (Ga, Mn)As are in excellent agreement with experimental data. Due to percolation effects and noncollinear magnetic structures at higher Mn concentrations, our calculations predict for (Ga, Mn)N very low Curie temperatures compared to mean-field estimates. 
S. Hilbert and W. Nolting