Phase-ordering kinetics of one-dimensional nonconserved scalar systems

We consider the phase-ordering kinetics of one-dimensional scalar systems. For attractive long-range (${\mathit{r}}^{\mathrm{-}(1+\mathrm{\sigma })}$) interactions with σ>0, ‘‘energy-scaling’’ arguments predict a growth law of the average domain size L∼${\mathit{t}}^{1/(1+\mathrm{\sigma })}$ for all σ>0. Numerical results for σ=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 σ→∞, and in that limit the amplitude of the growth law is exactly calculated.