  Using the N-patch renormalization group method we investigate the flow of the
quasiparticle weight in one-dimensional, weakly two-dimensional and fully
two-dimensional Hubbard models. In one dimension we reproduce the Luttinger
exponent that describes the disappearance of the quasiparticle peak towards
lower scales. Further we analyze effects of the band structure, interchain
hopping and the flow of the interactions in quasi-one-dimensional models. For
the two-dimensional case we study how the suppression of the quasiparticle
weight affects the flow to strong coupling. We find that the flow to strong
coupling remains essentially unchanged. This strengthens the evidence for
d-wave superconductivity in the weakly repulsive Hubbard model.
