  The effects of randomness and dimerization on the spin-1/2 XX chain are
studied by a mapping to free fermions. Results are presented for the transverse
and longitudinal components of the average and typical spin and string
correlation functions. Contrary to previous numerical evidence, the decay
exponents of all the above correlation functions are found to be in good
agreement with the theoretical RG predictions for the random singlet phase. We
also present cross-over functions for the above correlation functions in the
random dimer phase. Disorder averages have been taken for system sizes up to
N=1024, about ten times larger than in previous studies.
