Abstract
Previous calculations of a $t$-matrix approximation to Hubbard's model of a half-filled narrow energy band are extended to cover all possible occupancies. The method is exact in the low-density limit. The paramagnetic state is found to be more stable than in the Kanamori approximation. The nearly half-filled band, infinite-repulsion limit is also consistent with Nagaoka's prediction. The resulting phase transitions between paramagnetic, ferromagnetic, and antiferromagnetic states occur at smaller bandwidth/potential-energy ratios than those of Penn's Hartree-Fock approach.
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