  The two-dimensional antiferromagnetic S=1/2 Heisenberg model with random bond
dilution is studied using quantum Monte Carlo simulation at the percolation
threshold (50% of the bonds removed). Finite-size scaling of the staggered
structure factor averaged over the largest connected clusters of sites on L*L
lattices shows that long-range order exists within the percolating fractal
clusters in the thermodynamic limit. This implies that the order-disorder
transition driven by bond-dilution occurs exactly at the percolation threshold
and that the exponents are classical. This result should apply also to the
site-diluted system.
