Critical exponents in a transition between an AFM and a valence bond crystal

We 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. We 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. We also show the contrast between integer and half-integer spin cases.