  We prove that for quantum lattice systems in d<=2 dimensions the addition of
quenched disorder rounds any first order phase transition in the corresponding
conjugate order parameter, both at positive temperatures and at T=0. For
systems with continuous symmetry the statement extends up to d<=4 dimensions.
This establishes for quantum systems the existence of the Imry-Ma phenomenon
which for classical systems was proven by Aizenman and Wehr. The extension of
the proof to quantum systems is achieved by carrying out the analysis at the
level of thermodynamic quantities rather than equilibrium states.
