Ad. Rutenberg et Aj. Bray, PHASE-ORDERING KINETICS OF ONE-DIMENSIONAL NONCONSERVED SCALAR SYSTEMS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 50(3), 1994, pp. 1900-1911
We consider the phase-ordering kinetics of one-dimensional scalar syst
ems. 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 r
esults for a = 0.5, 1.0, and 1.5 demonstrate both scaling and the pred
icted growth laws. For purely short-range interactions, an approach of
Nagai and Kawasaki [Physica A 134, 483 (1986)] is asymptotically exac
t. For this case, the equal-time correlations scale, but the time-deri
vative correlations break scaling. The short-range solution also appli
es to systems with long-range interactions when sigma --> infinity, an
d in that limit the amplitude of the gowth law is exactly calculated.