  By the example of Heisenberg $d$-dimensional disordered non-frustrated
antiferromagnets, we discuss quantum transitions at $d\ge2$ from magnetically
ordered (superfluid) to various disorder-induced insulating phases (Bose-glass,
Mott-glass, etc.) in Bose systems with quenched disorder. We perform a scaling
consideration as well as a discussion based on the hydrodynamic description of
long-wavelength excitations and on the assumption that the ordered part of the
system shows fractal properties near the transition point. We propose that the
scaling ansatz for the singular part of the free energy suggested before for
the transition to the Bose-glass phase is applicable also for other transitions
if the quenched disorder does not produce a local imbalance in sublattices
magnetizations. We show using the scaling consideration that $\eta=2-z$ and
$\beta=\nu d/2$, where $\eta$, $\beta$, and $\nu$, are critical exponents of
the correlation function, the order parameter, and the correlation length,
respectively, and $z$ is the dynamical critical index. These relations were
missed in previous analytical discussions of Bose-glass and Mott-glass phases.
They signify, in particular, that $z=d/2$ for the transition to the Mott-glass
phase and that the density of states of localized excitations shows a
superuniversal (i.e., independent of $d$) behavior near the transitions. Being
derived solely from the scaling analysis, the above relations for $\eta$ and
$\beta$ are valid also for the transition to the random-singlet phase.
