Numerical study of multitime scaling in a solid system undergoing phase separation

The multitime-scaling rule for time correlation functions is shown in systems undergoing phase separation. With the use of multitime scaling, the asymptotic form of the structural function, S \~ (x) x^4, at small scaled wave numbers x is shown in a late state of phase separation in the diffusional system. A numerical simulation is performed to examine the multitime scaling. We use a discretized Cahn-Hilliard equation with the Oono-Puri free energy. The chemical potential is not conserved at all and may satisfy multitime scaling in the late stage of phase separation. Hence the suggested x^4 law of the structure function is justified.