  The spin-Peierls transition in the ground state of a quasi-one-dimensional
spin-1/2 Heisenberg model coupled to adiabatic bond phonons is studied using a
quantum Monte Carlo (QMC) method. The transition from a gapless Neel state to a
spin-gapped Peierls state is explored in the parameter space spanned by the
spatial anisotropy and the strength of spin-lattice coupling. It is found that
for any finite inter-chain coupling, the transition to a dimerized Peierls
ground state occurs only when the spin-lattice coupling exceeds a finite,
non-zero critical value. This is in contrast to the pure 1D model, where
adiabatic phonons lead to a dimerized ground state for any non-zero spin-phonon
coupling. The phase diagram in the above parameter space is mapped out. No
evidence is found for a region of co-existing long range magnetic order and
dimerization. The vanishing of the Neel order occurs simultaneously with the
setting in of the dimerization.
