Instabilities of weakly correlated electronic gas on a two dimensional lattice

We use the Kadanoff-Wilson renormalization group to find the instabilities of the two dimensional Hubbard model in the weak coupling limit. Starting from the full bandwidth, we reduce the energy cutoff for fermions and derive the low-energy effective action. If the filling is enough far from one half, the effective low-energy theory is BCS and there exists a mean-field like superconducting instability with D-wave order parameter. Close to the half-filling, the effective low-energy theory is parquet and the dominant fluctuations at the critical temperature are antiferromagnetic.