Classical percolation transition in the diluted two-dimensional S=1/2 Heisenberg antiferromagnet

The two-dimensional antiferromagnetic S=1/2 Heisenberg model with random site dilution is studied using quantum Monte Carlo simulations. Ground-state properties of the largest connected cluster on L×L lattices, with L up to 64, are calculated at the classical percolation threshold. In addition, clusters with a fixed number N_c of spins on an infinite lattice at the percolation density are studied for N_c up to 1024. The disorder averaged sublattice magnetization per spin extrapolates to the same nonzero infinite-size value for both types of clusters. Hence, the percolating clusters, which are fractal with dimensionality d=91/48, have antiferromagnetic long-range order. This implies that the order-disorder transition driven by site dilution occurs exactly at the percolation threshold and that the exponents are classical. The same conclusion is reached for the bond-diluted system. The full sublattice magnetization versus site dilution curve is obtained in terms of a decomposition into a classical geometrical factor and a factor containing all the effects of quantum fluctuations. The spin stiffness is shown to obey the same scaling as the conductivity of a random resistor network.