  Scaling relations are used to study cross-overs, due to anisotropic spin
interactions or single ion anisotropy, and due to disorder, in the
thermodynamics and correlation functions near quantum-critical transitions. The
principal results are simple with a wide range of applications. The region of
attraction to the stable anisotropic fixed point in the quantum-critical region
is exponentially enhanced by the dynamical critical exponent $z$ compared to
the region of attraction to the fixed point in the quantum disordered region.
The result implies that, even for small anisotropy, the region of attraction to
the stable incommensurate Ising or planar metallic anti-ferromagnetic critical
points, which belong to the universality class of the XY model with $z \to
\infty$, covers the entire quantum-critical region. In crossovers due to
disorder, the instability of the pure fixed point in the quantum disordered
region is exponentially enhanced by $z$ compared to that in the
quantum-critical region. This result suggests that for some classes of disorder
and for large enough $z$, one may find singularities in the correlations as a
function of frequency and temperature down to very low temperatures even though
the correlation length in space remains short range.
