Preasymptotic dynamical exponent in conserved order-parameter phase ordering dynamics

We study the approach of the dynamical exponent to (1/3 in phase ordering dynamics with conserved order parameter. We show that an extrapolation used to obtain the asymptotic dynamical exponent from kinetic Ising model simulations should be considered to be purely empirical; that is, contrary to what is usually stated, there is at present no known physical justification for the formula used in the extrapolation. In addition, we show that the empirical data are consistent with the Liftshitz-Slyozov mechanism being the only important ordering mechanism at late times, with the driving force being dependent on a modified curvature.