  We examine the phase diagram of a simple-cubic optical lattice half-filled by
two species of fermionic atoms with a repulsive s-wave contact interaction. We
use the Hartree approximation in the regime of weaker interactions, and a
Hubbard model approximation in the Mott insulating phase. The regime where the
Neel phase of this system is likely to be most accessible to experiments is at
intermediate lattice strengths and interactions, and our two approximations
agree fairly well in this regime. We discuss the various issues that may
determine where in this phase diagram the Neel phase is first produced and
detected experimentally, and analyze the quantum phases that occur in the
intermediate lattice strength regime.
