Weakly correlated electrons on a square lattice: A renormalization group theory

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Abstract
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.