  The weak coupling instabilities of a two dimensional Fermi system are
investigated for the case of a square lattice using a Wilson renormalization
group scheme to one loop order. We focus on a situation where the Fermi surface
passes through two saddle points of the single particle dispersion. In the case
of perfect nesting, the dominant instability is a spin density wave but d-wave
superconductivity as well as charge or spin flux phases are also obtained in
certain regions in the space of coupling parameters. The low energy regime in
the vicinity of these instabilities can be studied analytically. Although
saddle points play a major role (through their large contribution to the single
particle density of states), the presence of low energy excitations along the
Fermi surface rather than at isolated points is crucial and leads to an
asymptotic decoupling of the various instabilities. This suggests a more
mean-field like picture of these instabilities, than the one recently
established by numerical studies using discretized Fermi surfaces.
