Analytical treatments of interacting and disordered electron systems employ a perturbation theory assuming simultaneously weak disorder and weak interactions. Quite generally, these approaches break down near critical points, in particular near metal-insulator transitions, where the conductivity becomes small and the disorder no longer can be considered weak. Therefore, such methods cannot give unambiguous information about interaction effects in electron systems at or near the localization threshold. We start a longer term activity exploring a novel numerical technique along the lines of the functional renormalization group. The approach is perturbative in the interaction but (numerically) exact in the disorder. The goal is to study interaction effects on important localization transitions, including the integer quantum Hall transition and a newly predicted, self organized transition in the graphene material.
