Rounding of first order transitions in low-dimensional quantum systems with quenched disorder

We prove that the addition of an arbitrarily small random perturbation to a quantum spin system rounds a first-order phase transition in the conjugate order parameter in d≤2 dimensions, or for cases involving the breaking of a continuous symmetry in d≤4. This establishes rigorously for quantum systems the existence of the Imry-Ma phenomenon which for classical systems was proven by Aizenman and Wehr.