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

Nonperturbative Functional Renormalization Group for Random Field Models. III: Superfield formalism and ground-state dominance