  We develop a lattice mean field theory for ferromagnetic ordering in diluted
magnetic semiconductors by taking into account the spatial fluctuations
associated with random disorder in the magnetic impurity locations and the
finite mean free path associated with low carrier mobilities. Assuming a
carrier-mediated indirect RKKY exchange interaction among the magnetic
impurities, we find substantial deviation from the extensively used continuum
Zener model Weiss mean-field predictions. Our theory allows accurate analytic
predictions for Tc, and provides simple explanations for a number of observed
anomalies including the non-Brillouin function magnetization curves, the
suppressed low-temperature magnetization saturation, and the dependence of Tc
on conductivity.
