  For magnets with a fully frustrated inter-layer interaction, we argue that
the quantum phase transitions from a paramagnetic to an antiferromagnetic
ground state, driven by pressure or magnetic field, are asymptotically
three-dimensional, due to interaction-generated non-frustrated inter-layer
couplings. However, the relevant crossover scale is tiny, such that
two-dimensional behavior occurs in an experimentally relevant low-temperature
regime. In the pressure-driven case the phase transition may split, in which
case an Ising symmetry related to inter-layer bond order is broken before
magnetism occurs. We discuss the relation of our results to recent experiments
on BaCuSi2O6.
