We consider the properties of finite isotropic antiferromagnetic Heisenberg
chains with S=1/2,1,3/2 spins when a weak magnetic field is applied on a f
ew sites, using White's density-matrix renormalization-group method. For th
e S=l chain there exists only one length scale in the system which determin
es the behavior of the one- and two-point correlation functions both around
the local perturbation and near the free boundary. For the critical half-o
dd-integer spin cases the exponent of the spin-spin correlation function wa
s found to be eta =1 and the exponent of the decay of the site magnetizatio
n around the perturbed site is x(m) = eta/2 Close to a free boundary, howev
er, the behavior is completely different for S= 1/2 and S>1/2.