  Using a lattice-gas description of the low-energy degrees of freedom of the
quantum Heisenberg antiferromagnet on the frustrated two-leg ladder and bilayer
lattices we examine the magnetization process at low temperatures for these
spin models. In both cases the emergent discrete degrees of freedom implicate a
close relation of the frustrated quantum Heisenberg antiferromagnet to the
classical lattice gas with finite nearest-neighbor repulsion or, equivalently,
to the Ising antiferromagnet in a uniform magnetic field. Using this relation
we obtain analytical results for thermodynamically large systems in the
one-dimensional case. In the two-dimensional case we perform classical Monte
Carlo simulations for systems of up to $100 \times 100$ sites.
