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Ground-state energy of the d=1,2,3 dimensional Hubbard model in the weak-coupling limit.

The correlation energy of the Hubbard model on simple-cubic lattices is calculated in the weak-coupling regime for dimensions d=1,2,3. It is shown that, in spite of the nonanalytic dependences known to arise and in contrast to earlier expectations, the exact second-order contribution to the ground-state energy in d=1 can be obtained by ordinary perturbation theory. This result is argued to hold for any finite order and, in particular, for any dimension.