Critical Exponents in a Quantum Phase Transition of an Anisotropic 2D Antiferromagnet

I use the two-step density-matrix renormalization group method to extract the critical exponents $\beta$ and $\nu$ in the transition from a N'eel $Q=(\pi ,\pi )$ phase to a magnetically disordered phase with a spin gap. I find that the exponent $\beta$ computed from the magnetic side of the transition is consistent with that of the classical Heisenberg model, but not the exponent $z\nu$ computed from the disordered side. I also show the contrast between integer and half-integer spin cases.