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We have developed a nonperturbative functional renormalization group approachfor random field models and related disordered systems for which, due to theexistence of many metastable states, conventional perturbation theory oftenfails. The approach combines an exact renormalization group equation for theeffective average action with a nonperturbative approximation scheme based on adescription of the probability distribution of the renormalized disorderthrough its cumulants. For the random field $O(N)$ model, the minimaltruncation within this scheme is shown to reproduce the known perturbativeresults in the appropriate limits, near the upper and lower critical dimensionsand at large number $N$ of components, while providing a unifiednonperturbative description of the full $(N,d)$ plane, where $d$ is the spatialdimension.

Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. I: Effective Average Action Formalism