  Quasi-one-dimensional antiferromagnetic (AF) quantum spin systems show a wide
range of interesting phenomena such as the spin-Peierls transition and disorder
driven long range ordering. While there is no magnetic long range order in
strictly one-dimensional systems, in real systems some amount of interchain
coupling is always present and AF long range order may appear below a Neel
ordering temperature T_N. We study the effect of bond randomness on Neel
ordering in weakly coupled random AF S=1/2 chains both with and without
dimerization (or spin-Peierls order). We use the real space renormalization
group method to tackle the intrachain couplings, and a mean-field approximation
to treat the interchain coupling. We show that in the non-dimerized chain,
disorder (represented by bond randomness) enhances the Neel order parameter; in
the dimerized chain which shows no magnetic ordering in the weak interchain
coupling limit without randomness, disorder can actually lead to long range
order. Thus disorder is shown to lead to, or enhance the tendency toward long
range order, providing another example of the order-by-disorder phenomenon. We
make a qualitative comparison of our results with the observed phenomenon of
doping induced long range ordering in quasi-one-dimensional spin systems such
as CuGeO_3.
