  We study asymptotic expansions of spin-spin correlation functions for the XXZ
Heisenberg chain in the critical regime. We use the fact that the long-distance
effects can be described by the Gaussian conformal field theory. Comparing
exact results for form factors in the XYZ and sine-Gordon models, we determine
correlation amplitudes for the leading and main sub-leading terms in the
asymptotic expansions of spin-spin correlation functions. We also study the
isotropic (XXX) limit of these expansions.
