Renormalized mean-field analysis of antiferromagnetism and d-wave   superconductivity in the two-dimensional Hubbard model
  We analyze the competition between antiferromagnetism and superconductivity in the two-dimensional Hubbard model by combining a functional renormalization group flow with a mean-field theory for spontaneous symmetry breaking. Effective interactions are computed by integrating out states above a scale Lambda_{MF} in one-loop approximation, which captures in particular the generation of an attraction in the d-wave Cooper channel from fluctuations in the particle-hole channel. These effective interactions are then used as an input for a mean-field treatment of the remaining low-energy states, with antiferromagnetism, singlet superconductivity and triplet pi-pairing as the possible order parameters. Antiferromagnetism and superconductivity suppress each other, leaving only a small region in parameter space where both orders can coexist with a sizable order parameter for each. Triplet pi-pairing appears generically in the coexistence region, but its feedback on the other order parameters is very small. 
J. Reiss, D. Rohe, and W. Metzner