Accessing the Néel phase of ultracold fermionic atoms in a simple-cubic optical lattice

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 Néel 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 Néel phase is first produced and detected experimentally, and analyze the quantum phases that occur in the intermediate lattice strength regime.