of momentum cut-off and of non local disorder prevents the use of any [*exact*]{} methods, like the ones adopted in [@LFSG; @NTW; @ASZ; @Mu1; @Mu2], and one has therefore to rely on functional integral methods, which are more lengthy but of more general applicability. In particular we will use multiscale methods based on Wilsonian Renormalization Group (RG), in the more advanced form used in constructive Quantum Field Theory, see e.g. [@GJ]. Such form is exact, in the sense that the irrelevant terms (in the technical RG sense) are fully taken into account, while in most non exact RG implementations the irrelevant terms are simply neglected; as non local disorder or finite cut-offs are irrelevant in the infrared regime, non exact RG cannot distinguish between local and non local disorder, or the presence or absence of an ultraviolet cut-off.

Using the supersymmetric formalism we can rewrite disordered Dirac fermions in terms of functional integrals. The fermionic sector strongly reminds the [*non local Thirring model*]{} which was constructed using a multiscale analysis respectively in [@Le; @M2] for the ultraviolet problem and in [@M3] for the infrared part; therefore restricting to the fermionic sector a full non-perturbative construction of the model can be 