The field dependence of the ground state of semi-infinite uniaxial ant
iferromagnets and films is investigated in terms of a two-dimensional
area-preserving map, where the surfaces are introduced as appropriate
boundary conditions. For the film, the ground state is calculated for
any value of the number of planes in a very rapid and accurate way. Fo
r the semi-infinite system, we show that the so-called surface spin-fl
op state does not exist; by energetic arguments, we find that the inst
ability of the antiferromagnetic configuration leads to an interchange
of the sublattices. A nonhomogeneous ground state is instead found in
the bulk spin-flop phase.