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Exact results for curvature-driven coarsening in two dimensions

Jeferson J. Arenzon·Alan J. Bray·Leticia F. Cugliandolo·Alberto Sicilia
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Abstract

We consider the statistics of the areas enclosed by domain boundaries (`hulls') during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area that enclose an area greater than $A$ has, for large time $t$, the scaling form $N_h(A,t) = 2c/(A+λt)$, demonstrating the validity of dynamical scaling in this system, where $c=1/8π\sqrt{3}$ is a universal constant. Domain areas (regions of aligned spins) have a similar distribution up to very large values of $A/λt$. Identical forms are obtained for coarsening from a critical initial state, but with $c$ replaced by $c/2$.

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BibTeXRIS

Jeferson J. Arenzon, Alan J. Bray, Leticia F. Cugliandolo, Alberto Sicilia. 2007-01-24. Exact results for curvature-driven coarsening in two dimensions. https://doi.org/10.1103/physrevlett.98.145701

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