2026/07/20 by Tim R. Morris
#hep-th #cond-mat.stat-mech
We show that the derivative expansion of the exact (functional) renormalization group is a divergent series in any dimension, both for an exponential cutoff and more general smooth cutoffs. We prove this by showing that within massless λφ4 perturbation theory, such divergences arise first at two loops. From several lines of theoretical argument and by analysing infinite classes of two- and three-loop contributions, we conclude that the derivative expansion is an asymptotic series that initially converges towards the exact result before divergent behaviour takes over.