  By the example of Heisenberg $d$-dimensional disordered antiferromagnets, we
discuss quantum transitions at $d\ge2$ from magnetically ordered (superfluid)
to various disordered (insulating) glassy phases (Bose-glass, Mott-glass, etc.)
in Bose systems with quenched disorder. Our consideration is 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 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.
