  Quasi-one-dimensional quantum antiferromagnets formed by a d-dimensional
hypercubic lattice of weakly coupled spin-1/2 antiferromagnetic Heisenberg
chains are studied by combining exact results in one-dimension and
renormalization group analyses of the interchain correlations. It is shown that
d-dimensional magnetic long-range order develops at zero-temperature for
infinitesimal antiferromagnetic or ferromagnetic interchain couplings. In the
presence of weak bond alternations, the order-disorder transition occurs at a
finite interchain coupling. Relevances to the lightly doped quantum
antiferromagnets and multi-layer quantum Hall systems are discussed.
