The effect of quenched disorder on the low-energy and low-temperature properties of various two- and three-dimensional Heisenberg models is studied by a numerical strong disorder renormalization-group method. For strong enough disorder we have identified two relevant fixed points, in which the gap exponent, $\omega ,$ describing the low-energy tail of the gap distribution $P\left(\Delta \right)\sim {\Delta }^{\omega }$ is independent of disorder, the strength of couplings, and the value of the spin. The dynamical behavior of nonfrustrated random antiferromagnetic models is controlled by a singletlike fixed point, whereas for frustrated models the fixed point corresponds to a large spin formation and the gap exponent is given by $\omega \approx 0.$ Another type of universality class is observed at quantum critical points and in dimerized phases but no infinite randomness behavior is found, in contrast to that of one-dimensional models.

• Received 18 November 2002

DOI:https://doi.org/10.1103/PhysRevB.68.024424