  We reconsider the random bond antiferromagnetic spin-1/2 chain for weak
disorder and demonstrate the existence of crossover length scale x_W that
diverges with decreasing strength of the disorder. Recent DMRG calculations
[Phys. Rev. Lett. 89, 127202 (2002); cond-mat/0111027] claimed to have found
evidence for a non-universal behavior in this model and found no indications of
a universal infinite randomness fixed point (IRFP) scenario. We show that these
data are not in the asymptotic regime since the system sizes that have been
considered are of the same order of magnitude or much smaller than the
crossover length x_W. We give a scaling form for the xx-spin-correlation
function that takes this crossover length into account and that is compatible
with the IRFP scenario and a random singlet phase.
