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 (2008Phys.Rev.Lett.101127202), 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 ν 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 ν = 0.691(2) with that calculated in Wenzel (2008Phys.Rev.Lett.101127202). However, by using the data with a large number of spins N, we obtain ν = 0.707(6) which agrees with the most accurate Monte Carlo O(3) value ν = 0.7112(5) as well.