  We reformulate the nonperturbative functional renormalization group for the
random field Ising model in a superfield formalism, extending the
supersymmetric description of the critical behavior of the system first
proposed by Parisi and Sourlas [Phys. Rev. Lett. 43, 744 (1979)]. We show that
the two crucial ingredients for this extension are the introduction of a
weighting factor, which accounts for ground-state dominance when multiple
metastable states are present, and of multiple copies of the original system,
which allows one to access the full functional dependence of the cumulants of
the renormalized disorder and to describe rare events. We then derive exact
renormalization group equations for the flow of the renormalized cumulants
associated with the effective average action.
