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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 study a similar anisotropic spin-1/2Heisenberg model on the honeycomb lattice. The critical point where the phasetransition occurs due to the dimerization as well as the critical exponent$\nu$ are analyzed in great detail. Remarkly, using most of the available datapoints in conjunction with the expected finite-size scaling ansatz with asub-leading correction indeed leads to a consistent $\nu = 0.691(2)$ with thatcalculated in \cite{Wenzel08}. However by using the data with large number ofspins $N$, we obtain $\nu = 0.707(6)$ which agrees with the most accurate MonteCarlo O(3) value $\nu = 0.7112(5)$ as well.

Subtlety of Determining the Critical Exponent $\nu$ of the Spin-1/2 Heisenberg Model with a Spatially Staggered Anisotropy on the Honeycomb Lattice