  The ground-state properties of the spin-1/2 antiferromagnetic Heisenberg
model with spatially anisotropic couplings on a square lattice are investigated
by a spin-rotation-invariant Green's-function approach and by Lanczos
diagonalizations on lattices up to 36 sites supplemented by finite-size
scaling. We focus on the anisotropy-driven transition from the N\'eel state to
a paramagnetic state with antiferromagnetic short-range order and on the
spatial dependence of spin correlation functions. Our principal result is that
a rather sharp crossover in the magnetic behavior occurs at the coupling ratio
$R_0\simeq 0.2$ ($R=J_y/J_x$).
