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

Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we re-investigate the phase transition of this model induced by dimerization. We focus on studying the finite-size scaling of the observables $\rho_{s1} L$ and $\rho_{s2} L$, where $L$ stands for the spatial 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-size scaling using the observable $\rho_{s2} L$, which corresponds to the spatial direction with a fixed antiferromagnetic coupling, one would suffer a much less severe 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 analysis concerning the limitation for the availability of large volumes data in our study. Remarkably, by employing the method of fixing the aspect-ratio of spatial winding numbers squared in the simulations, even from $\rho_{s1} L$ which receives the most serious correction among the observables considered in this study, we arrive at a value for the critical exponent $\nu$ which is consistent with the expected O(3) value by using only up to $L = 64$ data points.