Planar and lamellar antiferromagnetism in Hubbard models

The Hubbard model with extended hoppings on a cubic lattice is shown to hav e antiferromagnetic phases displaying long-range order, when the temperatur e is small and the repulsive Coulomb potential is sufficiently strong. Our results are rigorous in the case of the asymmetric Hubbard model. Besides c hessboard states, stabilizing effects of hopping yield other phases, such a s planar and lamellar ones, depending on the relative strength of the hoppi ng coefficients.