  We study by the perturbative Functional Renormalization Group (FRG) the
Random Field and Random Anisotropy O(N) models near $d=4$, the lower critical
dimension of ferromagnetism. The long-distance physics is controlled by
zero-temperature fixed points at which the renormalized effective action is
nonanalytic. We obtain the beta functions at 2-loop order, showing that despite
the nonanalytic character of the renormalized effective action, the theory is
perturbatively renormalizable at this order. The physical results obtained at
2-loop level, most notably concerning the breakdown of dimensional reduction at
the critical point and the stability of quasi-long range order in $d<4$, are
shown to fit into the picture predicted by our recent non-perturbative FRG
approach.
