Subtlety of determining the critical exponent ν of the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the honeycomb 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 Wenzel (2008 Phys. Rev. Lett. 101 127202), we study a similar anisotropic spin-1/2 Heisenberg model on the honeycomb lattice. The critical point where the phase transition occurs due to the dimerization as well as the critical exponent. are analyzed in great detail. Remarkably, using most of the available data points in conjunction with the expected finite-size scaling ansatz with a sub-leading correction indeed leads to a consistent nu = 0.691(2) with that calculated in Wenzel (2008 Phys. Rev. Lett. 101 127202). However, by using the data with a large number of spins N, we obtain nu = 0.707(6) which agrees with the most accurate Monte Carlo O(3) value. = 0.7112(5) as well.