Dynamical scaling functions in conserved vector order-parameter systems without topological defects

We study the growth of order following a zero temperature quench in the one-dimensional XY (n=2) and Heisenberg (n=3) models and in the two-dimensional n=4 model with a conserved order parameter using a Langevin formalism. These systems are characterized by an absence of localized topological defects (n>d). Although the structure factor S(k,t) obeys standard dynamical scaling at late times, we show quite convincingly that S(k,t) possesses an exponential tail, violating the generalized Porod's law. We also find that the form of the asymptotic correlation function at small distances exhibits a striking universality