  We present a systematic study of the anisotropic spin-1/2 Heisenberg model in
staggered magnetic fields in two dimensions (2D). To mimic real materials, we
consider a system of coupled, antiferromagnetic chains, whose interchain
interaction can be either ferro- or antiferromagnetic. When the staggered field
is commensurate with the magnetic interactions, an energy gap opens immediately
and follows a power law as a function of the applied field, similar to the
situation in 1D. When the field competes with the interactions, a quantum phase
transition (QPT) occurs from a gapless, magnetically ordered phase at low
fields to a gapped, disordered regime. We use a continuous-time Monte Carlo
method to compute the staggered moment of the ordered phases and the spin gap
of the disordered phases. We deduce the phase diagrams as functions of the
anisotropy ratio and the applied field, and calculate the scaling behavior of
the models in both quantities. We show that in the competitive case, the
staggered field acts to maintain a regime of quasi-1D behavior around the QPT,
and we discuss as a consequence the nature of the crossover from 1D to 2D
physics.
