  The interplay between the singlet ground state of the antiferromagnetic
Heisenberg model and the experimentally measured N\'eel state of
antiferromagnets is studied. To verify the hypothesis [M. I. Katsnelson et al.,
Phys. Rev. B 63, 212404 (2001)] that the latter can be considered to be a
result of local measurements destroying the entanglement of the quantum ground
state, we have performed systematic simulations of the effects of von
Neumannmeasurements for the case of a one-dimensional antiferromagnetic
spin-1/2 system for various types and degrees of magnetic anisotropies. It is
found that in the ground state, a magnetization measurement can create
decoherence waves [M. I. Katsnelson et al. Phys. Rev. A 62, 022118 (2000)] in
the magnetic sublattices, and that a symmetry breaking anisotropy does not lead
to alignment of the spins in a particular direction. However, for an easy-axis
anisotropy of the same order magnitude as the exchange constant, a measurement
on the singlet ground state can create N\'eel-ordering in finite systems of
experimentally accessible size.
