Quantum vs. Geometric Disorder in a Two-Dimensional Heisenberg Antiferromagnet

We present a numerical study of the spin-1/2 bilayer Heisenberg antiferromagnet with random interlayer dimer dilution. From the temperature dependence of the uniform susceptibility and a scaling analysis of the spin correlation length we deduce the ground state phase diagram as a function of nonmagnetic impurity concentration p and bilayer coupling g. At the site percolation threshold, there exists a multicritical point at small but nonzero bilayer coupling g_m = 0.15(3). The magnetic properties of the single-layer material La_2Cu_{1-p}(Zn,Mg)_pO_4 near the percolation threshold appear to be controlled by the proximity to this new quantum critical point.