  Using a numerical implementation of strong disorder renormalization group, we
study the low-energy, long-distance properties of layers and bilayers of $S =
1/2$ Heisenberg antiferromagnets with different type of disorder: bond
randomness, site and dimer dilution. Generally the systems exhibit an ordered
and a disordered phase separated by a phase boundary on which the static
critical exponents appear to be independent of bond randomness in the strong
disorder regime, while the dynamical exponent is a continuous function of the
bond disorder strength. The low-energy fixed points of the off-critical phases
are affected by the actual form of the disorder, and the disorder induced
dynamical exponent depends on the disorder strength. As the strength of bond
disorder is increased, there is a set of crossovers in the properties of the
low-energy singularities. For weak disorder quantum fluctuations play the
dominant role. For intermediate disorder non-localized disorder fluctuations
are relevant, which become localized for even stronger bond disorder. We also
present some quantum Monte Carlo simulations results to support the strong
disorder renormalization approach.
