  It is shown that in the two-dimensional attractive Hubbard model, the
mean-field phase transition is replaced by a renormalized classical regime of
fluctuations where a pseudogap opens up in the single-particle spectral weight.
It is argued that this pseudogap and precursors of the ordered state
quasiparticles can occur only in strongly anisotropic quasi two-dimensional
materials. This precursor phenomenon differs from preformed local pairs.
Furthermore, while critical antiferromagnetic fluctuations would also lead to a
pseudogap in the repulsive model, there are some important differences between
the superconducting and magnetic pseudogap.
