  We study the possibility of d0 ferromagnetism in the compound
  MgO doped with nitrogen (N). The Haldane-Anderson impurity model is
formulated within the tight-binding approximation for determining the host
band-structure and the impurity-host hybridization. Using the quantum Monte
Carlo technique, we observe a finite local moment for an N impurity, and
long-range ferromagnetic correlations between two N impurities. The
ferromagnetic correlations are strongly influenced by the impurity bound state.
When the ferromagnetic correlation between a pair of impurities is mapped onto
the isotropic Heisenberg model for two spin-1/2 particles, the effective
exchange constant J12 is found to increase with increasing temperature. Similar
temperature dependence of J12 is also obtained in other diluted magnetic
semiconductors, such as zincblende ZnO doped with Mn. The temperature
dependence of J12 suggests that the mapping of the full Hamiltonian onto the
spin Hamiltonian cannot fully describe the magnetic correlations for the
diluted magnetic semiconductors at least in the limit of low impurity spin.
