Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems

Details Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems

1994-04-15

arxiv.org/abs/cond-mat/9404046v1

Phys. Rev. E vol. 50, p. 1900 (1994)

Physics

Condensed Matter

19 pages, RevTex 3.0, 8 FIGURES UPON REQUEST, 15494

Scientific paper

10.1103/PhysRevE.50.1900

We consider the phase-ordering kinetics of one-dimensional scalar systems. For attractive long-range ($r^{-(1+\sigma)}$) interactions with $\sigma>0$, ``Energy-Scaling'' arguments predict a growth-law of the average domain size $L \sim t^{1/(1+\sigma)}$ for all $\sigma >0$. Numerical results for $\sigma=0.5$, $1.0$, and $1.5$ demonstrate both scaling and the predicted growth laws. For purely short-range interactions, an approach of Nagai and Kawasaki 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 $\sigma \rightarrow \infty$, and in that limit the amplitude of the growth law is exactly calculated.

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