Kinetics of phase-separation in the critical spherical model and local scale-invariance

The scaling forms of the space- and time-dependent two-time correlation and response functions are calculated for the kinetic spherical model with a conserved order-parameter and quenched to its critical point from a completely disordered initial state. The stochastic Langevin equation can be split into a noise part and into a deterministic part which has local scale-transformations with a dynamical exponent z=4 as a dynamical symmetry. An exact reduction formula allows to express any physical average in terms of averages calculable from the deterministic part alone. The exact spherical model results are shown to agree with these predictions of local scale-invariance. The results also include kinetic growth with mass conservation as described by the Mullins-Herring equation.