Magnetic and Superconducting Instabilities of the Hubbard Model at the Van Hove Filling

We use a novel temperature-flow renormalization group technique to analyze magnetic and superconducting instabilities in the two-dimensional ${t-t}^{\prime }$ Hubbard model for particle densities close to the Van Hove filling as a function of the next-nearest-neighbor hopping $t^{\prime }$. In the one-loop flow at the Van Hove filling, the characteristic temperature for the flow to strong coupling is suppressed drastically around $t_c^{\prime }\approx -0.33t$, suggesting a quantum critical point between $d$-wave pairing at moderate $t^{\prime }>t_c^{\prime }$ and ferromagnetism for $t^{\prime }<t_c^{\prime }$. Upon increasing the particle density in the latter regime, the leading instability occurs in the triplet pairing channel.