  We investigate the behavior of antiferromagnetic integer-spin chains in a
staggered magnetic field, by means of the density-matrix renormalization group,
carefully addressing the role of finite-size effects within the Haldane phase
at small fields. In the case of spin S=2, we determine the dependence of the
groundstate energy and magnetization on the external field, in the
thermodynamic limit, and show how the peculiar finite-size behavior can be
connected with the crossover in the groundstate from a spin liquid to a
polarized N\'eel state.
