  We present numerical results for an $S=1/2$ Heisenberg antiferromagnet on a
inhomogeneous square lattice with tunable interaction between spins belonging
to different plaquettes. Employing Quantum Monte Carlo, we significantly
improve on previous results for the the critical point separating
singlet-disordered and N\'{e}el-ordered phases, and obtain an estimate for the
critical exponent $\nu$ consistent with the three-dimensional classical
Heisenberg universality class. Additionally, we show that a fairly accurate
result for the critical point can be obtained from a Contractor Renormalization
(CORE) expansion by applying a surprisingly simple analysis to the effective
Hamiltonian.
