Unwinding Scaling Violations in Phase Ordering

Abstract

The one-dimensional $O(2)$ model is the simplest example of a system with topological textures. The model exhibits anomalous ordering dynamics due to the appearance of two characteristic length scales: the phase coherence length, $L \sim t^{1/z}$, and the phase winding length, $L_{w} \sim L^χ$. We derive the scaling law $z=2+μχ$, where $μ=0$ ($μ=2$) for nonconserved (conserved) dynamics and $χ=1/2$ for uncorrelated initial orientations. From hard-spin equations of motion, we consider the evolution of the topological defect density and recover a simple scaling description. (please email ar@v2.ph.man.ac.uk for a hard copy by mail)