  Corrections to the asymptotic correlation function in a Heisenberg spin-1/2
antiferromagnetic spin chain are known to vanish slowly (logarithmically) as a
function of the distance r or the chain size L. This leads to significant
differences with numerical results. We calculate the sub-leading logarithmic
corrections to the finite-size correlation function, using renormalization
group improved perturbation theory, and compare the result with numerical data.
