The renormalization group flow in field theories with quenched disorder

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In this paper we analyze the renormalization group (RG) flow of field theories with quenched disorder, in which the couplings vary randomly in space.

• We analyze both classical (Euclidean) disorder and quantum disorder, emphasizing general properties rather than specific cases.
• The RG flow of the disorder-averaged theories takes place in the space of their coupling constants and also in the space of distributions for the disordered couplings, and the two mix together.
• We write down a generalization of the Callan-Symanzik equation for the flow of disorder-averaged correlation functions.