  A theoretical description is presented for low-temperature magnetic-field
induced three-dimensional (3D) ordering transitions in strongly anisotropic
quantum antiferromagnets, consisting of weakly coupled antiferromagnetic
spin-1/2 chains and ladders. First, effective continuum field theories are
derived for the one-dimensional subsystems. Then the Luttinger parameters,
which determine the low-temperature susceptibilities of the chains and ladders,
are calculated from the Bethe ansatz solution for these effective models. The
3D ordering transition line is obtained using a random phase approximation for
the weak inter-chain (inter-ladder) coupling. Finally, considering a Ginzburg
criterion, the fluctuation corrections to this approach are shown to be small.
The nature of the 3D ordered phase resembles a Bose condensate of integer-spin
magnons. It is proposed that for systems with higher spin degrees of freedom,
e.g. N-leg spin-1/2 ladders, multi-component condensates can occur at high
magnetic fields.
