  Critical behavior of the quantum phase transition of a site-diluted
Heisenberg antiferromagnet on a square lattice is investigated by means of the
quantum Monte Carlo simulation with the continuous-imaginary-time loop
algorithm. Although the staggered spin correlation function decays in a power
law with the exponent definitely depending on the spin size $S$, the
correlation-length exponent is classical, i.e., $\nu=4/3$. This implies that
the length scale characterizing the non-universal quantum phase transition is
nothing but the mean size of connected spin clusters.
