  Using holographic duality, we present an analytically controlled theory of
quantum critical points without quasiparticles, at finite disorder and finite
charge density. These fixed points are obtained by perturbing a disorder-free
quantum critical point with relevant disorder whose operator dimension is
perturbatively close to Harris marginal. We analyze these fixed points both
using field theoretic arguments, and by solving the bulk equations of motion in
holography. We calculate the critical exponents of the IR theory, together with
thermoelectric transport coefficients. Our predictions for the critical
exponents of the disordered fixed point are consistent with previous work, both
in holographic and nonholograpic models.
