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Maximizing the Neel temperature of fermions in a simple-cubic optical lattice

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.