  Three-dimensional magnetic ordering transitions are studied theoretically in
strongly anisotropic quantum magnets. An external magnetic field can drive
quasi-one-dimensional subsystems with a spin gap into a gapless regime, thus
inducing long-range three-dimensional magnetic ordering due to weak residual
magnetic coupling between the subsystems. Compounds with higher spin degrees of
freedom, such as N-leg spin-1/2 ladders, are shown to have cascades of ordering
transitions. At high magnetic fields, zero-point fluctuations within the
quasi-1D subsystems are suppressed, causing quantum corrections to the ordering
temperature to be reduced.
