Ferromagnetism in diluted magnetic semiconductors at low carrier density

We present a general approach to the problem of a ferromagnetic phase transition in diluted magnetic semiconductors with free carriers. The Curie temperature of ferromagnetic transition is calculated in the mean field approximation. The approach allows to analyze the effects of magnetic fluctuations and disorder on the Curie temperature. We also propose a new mechanism of exchange interaction between magnetic impurities at vanishing concentration of free carriers.