  Motivated by the unexpected Monte Carlo results as well as the theoretical
proposal of a large correction to scaling for the critical theory of the 2-d
staggered-dimer spin-1/2 Heisenberg model on the square lattice, we study the
phase transitions induced by dimerization of several dimerized quantum
Heisenberg models with spatial anisotropy using first principles Monte Carlo
method. Remarkably, while our Monte Carlo data for all the models considered
here, including the herringbone- and ladder-dimer models on the square lattice,
are compatible with the recently proposed scenario of an enhanced correction to
scaling, we find it is likely that the enhanced correction to scaling manifests
itself as amplification of the nonuniversal prefactors appeared in the scaling
forms. In other words, our data are in consistence with the established
numerical values for the critical exponents, including the confluent exponent,
in the O(3) universality class. Convincing numerical evidence is provided to
support this proposed scenario.

Strongly Correlated Electrons;High Energy Physics - Lattice