Bond-randomness-induced Neel order in weakly coupled antiferromagnetic spin chains

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.