  We study two planar square lattice Heisenberg models with explicit
dimerization or quadrumerization of the couplings in the form of ladder and
plaquette arrangements. We investigate the quantum critical points of those
models by means of (stochastic series expansion) quantum Monte Carlo
simulations as a function of the coupling ratio $\alpha = J^\prime/J$. The
critical point of the order-disorder quantum phase transition in the ladder
model is determined as $\alpha_\mathrm{c} = 1.9096(2)$ improving on previous
studies. For the plaquette model we obtain $\alpha_\mathrm{c} = 1.8230(2)$
establishing a first benchmark for this model from quantum Monte Carlo
simulations. Based on those values we give further convincing evidence that the
models are in the three-dimensional (3D) classical Heisenberg universality
class. The results of this contribution shall be useful as references for
future investigations on planar Heisenberg models such as concerning the
influence of non-magnetic impurities at the quantum critical point.
