Defect Relaxation and Coarsening Exponents

TL;DR

This paper investigates how defect relaxation rates influence the growth of order in systems transitioning from disordered to ordered phases, analyzing different symmetries, dynamics, and interaction ranges.

Contribution

It provides a unified framework linking defect relaxation decay rates to coarsening exponents across various symmetries and dynamics.

Findings

Coarsening scale L(t) scales as t^(1/z) from relaxation decay rate omega(k) ~ k^z.

Results agree with earlier energy scaling analyses.

Analysis includes effects of infrared divergences and different interaction ranges.

Abstract

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.