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Theory of phase ordering kinetics

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  • Bray, A.J.

Abstract

The theory of phase ordering kinetics is reviewed, and new results for systems with continuous symmetry presented. A generalisation of “Porod's law” for the tail of the structure factor, of the form S(k, t) ∼ k−(d+n)L(t)−n for kL(t) ≫ 1, where L(t) is the characteristic length scale at time t after the quench, is derived where, for a vector order parameter, n is simply the number of components of the vector. The power-law tail is shown to be associated with topological defects in the field, and its amplitude is calculated exactly in terms of the defect density. For a conserved vector order parameter the multiscaling form obtained for n = ∞ is argued to be special to this limit. Using an approximate theory due to Mazenko, it is shown that conventional scaling is recovered, for any finite n, when t→∞, with L(t)∼ (tln n)14 for n large.

Suggested Citation

  • Bray, A.J., 1993. "Theory of phase ordering kinetics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 194(1), pages 41-52.
    • Handle: RePEc:eee:phsmap:v:194:y:1993:i:1:p:41-52
    DOI: 10.1016/0378-4371(93)90338-5
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    Cited by:

    1. Leclaire, Sébastien & Pellerin, Nicolas & Reggio, Marcelo & Trépanier, Jean-Yves, 2014. "Multiphase flow modeling of spinodal decomposition based on the cascaded lattice Boltzmann method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 307-319.

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