Theory of phase ordering kinetics

A.J. Bray

Physica A: Statistical Mechanics and its Applications, 1993, vol. 194, issue 1, 41-52

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.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:194:y:1993:i:1:p:41-52

DOI: 10.1016/0378-4371(93)90338-5

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