  The density-matrix renormalization-group technique is used to calculate the
spin correlation functions <S^x_jS^x_k> and <S^z_jS^z_k> of the one-dimensional
S=1/2 XXZ model in the gapless regime. The numerical results for open chains of
200 spins are analyzed by comparing them with correlation functions calculated
from a low-energy field theory. This gives precise estimates of the amplitudes
of the correlation functions in the thermodynamic limit. The exact amplitude
recently conjectured by Lukyanov and Zamolodchikov and the logarithmic
correction in the Heisenberg model are confirmed numerically.
