  For a simple-cubic optical lattice with lattice spacing d, occupied by two
species of fermionic atoms of mass m that interact repulsively, we ask what
conditions maximize the Neel temperature in the Mott insulating phase at
density one atom per site, with equal numbers of the two species. This maximum
occurs near the edge of the regime where the system is well-approximated by the
usual Hubbard model. The correction to the Hubbard-model approximation that
produces a "direct" ferromagnetic interaction between atoms in nearest-neighbor
Wannier orbitals is the leading term that limits how high the Neel temperature
can be made.
