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Puzzled by the indication of a new critical theory for the spin-1/2Heisenberg model with a spatially staggered anisotropy on the square lattice assuggested in \cite{Wenzel08}, we re-investigate the phase transition of thismodel induced by dimerization. We focus on studying the finite-size scaling ofthe observables $\rho_{s1} L$ and $\rho_{s2} L$, where $L$ stands for thespatial box sizes used in the simulations and $\rho_{si}$ with $i \in \{1,2\}$is the spin-stiffness in $i$-direction. We find by performing finite-sizescaling using the observable $\rho_{s2} L$, which corresponds to the spatialdirection with a fixed antiferromagnetic coupling, one would suffer a much lesssevere correction compared to that of using $\rho_{s1} L$. Therefore $\rho_{s2}L$ is a better quantity than $\rho_{s1} L$ for finite-size scaling analysisconcerning the limitation for the availability of large volumes data in ourstudy. Remarkably, by employing the method of fixing the aspect-ratio ofspatial winding numbers squared in the simulations, even from $\rho_{s1} L$which receives the most serious correction among the observables considered inthis study, we arrive at a value for the critical exponent $\nu$ which isconsistent with the expected O(3) value by using only up to $L = 64$ datapoints.

The Phase Transition of the Spin-1/2 Heisenberg Model with a Spatially Staggered Anisotropy on the Square Lattice