Paramagnetic and Antiferromagnetic Phases in the Half-Filled Narrow Energy Band

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Abstract
The effect of correlation on the antiferromagnetic and paramagnetic phases of Hubbard's model of a half-filled narrow band are investigated using second-order perturbation theory. Employing the gap of the antiferromagnetic state as a variational parameter, it is shown that the increase of the bandwidth/potential-energy ratio leads to a phase transition into the paramagnetic state nearly where Mott has estimated it to occur. The convergence of the perturbation expansion is shown to be excellent at the transition.