Defect Relaxation and Coarsening Exponents

Details Defect Relaxation and Coarsening Exponents Defect Relaxation and Coarsening Exponents

1998-02-17

arxiv.org/abs/cond-mat/9802183v1

Phys. Rev. E 58, 1508 (1998)

Physics

Condensed Matter

Statistical Mechanics

Revtex, 7 pages, no figures, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.58.1508

The coarsening exponents describing the growth of long-range order in systems quenched from a disordered to an ordered phase are discussed in terms of the decay rate, omega(k), for the relaxation of a distortion of wavevector k applied to a topological defect. For systems described by order parameters with Z(2) (`Ising'), and O(2) (`XY') symmetry, the appropriate defects are domain walls and vortex lines respectively. From omega(k) ~ k^z, we infer L(t) ~ t^(1/z) for the coarsening scale, with the assumption that defect relaxation provides the dominant coarsening mechanism. The O(2) case requires careful discussion due to infrared divergences associated with the far field of a vortex line. Conserved, non-conserved, and `intermediate' dynamics are considered, with either short-range or long-range interactions. In all cases the results agree with an earlier `energy scaling' analysis.

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