  We study the weakly interacting Hubbard model on the square lattice using a
one-loop renormalization group approach. The transition temperature T_c between
the metallic and (nearly) ordered states is found. In the parquet regime, (T_c
>> |mu|), the dominant correlations at temperatures below T_c are
antiferromagnetic while in the BCS regime (T_c << |mu|) at T_c the d-wave
singlet pairing susceptibility is most divergent.
