  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(Delta) ~ Delta^omega is independent of disorder, the strength of couplings
and the value of the spin. The dynamical behavior of non-frustrated random
antiferromagnetic models is controlled by a singlet-like fixed point, whereas
for frustrated models the fixed point corresponds to a large spin formation and
the gap exponent is given by omega ~ 0. Another type of universality classes is
observed at quantum critical points and in dimerized phases but no infinite
randomness behavior is found, in contrast to one-dimensional models.
