Renormalization group analysis of magnetic and superconducting instabilities near van Hove band fillings

Phase diagrams of the two-dimensional one-band t-t^' Hubbard model are obtained within the two-patch and temperature-cutoff many-patch renormalization group approaches. At small t^' and at van Hove band fillings antiferromagnetism dominates, while with increasing t^' or changing filling antiferromagnetism is replaced by d-wave superconductivity. Near t^'=t/2 and close to van Hove band fillings the system is unstable towards ferromagnetism. Away from van Hove band fillings this ferromagnetic instability is replaced by a region with dominating triplet p-wave superconducting correlations. The results of the renormalization-group approach are compared with the mean-field results and the results of the T-matrix approximation.