PHASE-ORDERING KINETICS OF ONE-DIMENSIONAL NONCONSERVED SCALAR SYSTEMS

We consider the phase-ordering kinetics of one-dimensional scalar systems. For attractive long-range (r(-(1+sigma)) interactions with sigma > O, ''energy-scaling'' arguments predict a growth law of the average domain size L similar to t(1/(1+sigma)) for all sigma > O. Numerical results for a = 0.5, 1.0, and 1.5 demonstrate both scaling and the predicted growth laws. For purely short-range interactions, an approach of Nagai and Kawasaki [Physica A 134, 483 (1986)] is asymptotically exact. For this case, the equal-time correlations scale, but the time-derivative correlations break scaling. The short-range solution also applies to systems with long-range interactions when sigma --> infinity, and in that limit the amplitude of the gowth law is exactly calculated.