Temperature-flow renormalization group and the competition between superconductivity and ferromagnetism - art. no. 184516

We derive a differential equation for the one-particle-irreducible vertex f unctions of interacting fermions as a function of the temperature. Formally , these equations correspond to a Wilsonian renormalization group (RG) sche me that uses the temperature as an explicit scale parameter. Our method all ows us to analyze the competition between superconducting and various magne tic Fermi surface instabilities in the one-loop approximation. In particula r, this includes ferromagnetic fluctuations, which are difficult to treat o n an equal footing in conventional Wilsonian momentum space techniques. App lying the scheme to the two-dimensional t-t' Hubbard model we investigate t he RG flow of the interactions at the van Hove filling with varying next-ne arest-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.