Two-dimensional non-Fermi liquids with quenched disorder

Despite significant theoretical progress, the effect of quenched disorder on non-Fermi liquids with a finite density of fermions interacting with soft order parameter fluctuations near a quantum critical point remains poorly understood. We study the interplay of disorder and interactions in the exactly solvable "matrix large N" non-Fermi liquid model in two spatial dimensions. We investigate the stability of the corresponding strongly interacting fixed point and show that diffusive effects drastically modify the properties of the critical regime and associated critical exponents.