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 < or = 2 dimensions, or for cases involving the breaking of a continuous symmetry in d < or = 4. This establishes rigorously for quantum systems the existence of the Imry-Ma phenomenon which for classical systems was proven by Aizenman and Wehr.