Temperature-flow renormalization group and the competition between superconductivity and ferromagnetism

We derive a differential equation for the one-particle-irreducible vertex functions of interacting fermions as a function of the temperature. Formally, these equations correspond to a Wilsonian renormalization group (RG) scheme that uses the temperature as an explicit scale parameter. Our method allows us to analyze the competition between superconducting and various magnetic Fermi surface instabilities in the one-loop approximation. In particular, this includes ferromagnetic fluctuations, which are difficult to treat on an equal footing in conventional Wilsonian momentum space techniques. Applying the scheme to the two-dimensional t-t' Hubbard model we investigate the RG flow of the interactions at the van Hove filling with varying next-nearest-neighbor hopping t'. Starting at t' = 0 we describe the evolution of the flow to strong coupling from an antiferromagnetic nesting regime over a d-wave regime at moderate t' to a ferromagnetic region at larger absolute values of t'. Upon increasing the particle density in the latter regime the ferromagnetic tendencies are cut off and the leading instability occurs in the triplet superconducting pairing channel.