The Energy-Scaling Approach to Phase-Ordering Growth Laws

Details The Energy-Scaling Approach to Phase-Ordering Growth Laws The Energy-Scaling Approach to Phase-Ordering Growth Laws

1994-09-21

arxiv.org/abs/cond-mat/9409088v2

Phys. Rev. E vol. 51, p. 5499 (1995)

Physics

Condensed Matter

LATeX 18 pages (REVTeX macros), one postscript figure appended, REVISED --- rearranged and clarified, new paragraph on naive d

Scientific paper

10.1103/PhysRevE.51.5499

We present a simple, unified approach to determining the growth law for the characteristic length scale, $L(t)$, in the phase ordering kinetics of a system quenched from a disordered phase to within an ordered phase. This approach, based on a scaling assumption for pair correlations, determines $L(t)$ self-consistently for purely dissipative dynamics by computing the time-dependence of the energy in two ways. We derive growth laws for conserved and non-conserved $O(n)$ models, including two-dimensional XY models and systems with textures. We demonstrate that the growth laws for other systems, such as liquid-crystals and Potts models, are determined by the type of topological defect in the order parameter field that dominates the energy. We also obtain generalized Porod laws for systems with topological textures.

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