  The random antiferromagnetic spin-1/2 XX and XXZ chain is studied numerically
for varying strength of the disorder, using exact diagonalization and
stochastic series expansion methods. The spin-spin correlation function as well
as the stiffness display a clear crossover from the pure behavior (no disorder)
to the infinite randomness fixed point or random singlet behavior predicted by
the the real space renormalization group. The crossover length scale is shown
to diverge as $\xi\sim{\mathcal D}^{-\gamma}$, where ${\mathcal D}$ is the
variance of the random bonds. Our estimates for the exponent $\gamma$ agrees
well within the error bars with the one for the localization length exponent
emerging within an analytical bosonization calculation. Exact diagonalization
and stochastic series expansion results for the string correlation function are
also presented.
