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Abstract |
We will 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. We find that local operators can mix with the response of the theory to
local changes in the disorder distribution, and that the generalized Callan-Symanzik equation
mixes the disorder averages of several different correlation functions. For classical disorder
we show that this can lead to new types of anomalous dimensions and to logarithmic behavior
at fixed points. For quantum disorder we find that the RG flow always generates a rescaling of
time relative to space, which at a fixed point generically leads to Lifshitz scaling. The
dynamical scaling exponent z behaves as an anomalous dimension and we compute it at
leading order in perturbation theory in the disorder for a general theory. We also find in
quantum disorder that local operators mix with non-local (in time) operators under the RG,
and that there are critical exponents associated with the disorder distribution that have not
previously been discussed. |
