  Dangling edge spins of dimerized two-dimensional spin-1 Heisenberg
antiferromagnets are shown to exhibit nonordinary quantum critical
correlations, akin to the scaling behavior observed in recently explored
spin-1/2 systems. Based on large-scale quantum Monte Carlo simulations, we
observe remarkable similarities between these two cases, and also examine the
crossover to the fundamentally distinct behavior in the one-dimensional limit
of strongly coupled edge spins. We complement our numerical analysis by a
cluster mean-field theory that encompasses the qualitatively similar behavior
for the spin-1 and the spin-1/2 case, and its dependence on the spatial edge
spin configuration in a generic way.
