Four-point vertex in the Hubbard model and partial bosonization

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Magnetic and superconducting instabilities in the two-dimensional t-t'-Hubbard model are discussed within a functional renormalization group approach. The fermionic four-point vertex is efficiently parametrized by means of partial bosonization. The exchange of composite bosons in the magnetic, charge density and superconducting channels accounts for the increase of the effective couplings with increasing length scale. We compute the pseudocritical temperature for the onset of local order in various channels.