Unwinding Scaling Violations in Phase Ordering

TL;DR

This paper investigates the anomalous ordering dynamics in the one-dimensional $O(2)$ model, revealing how two characteristic length scales evolve and deriving a new scaling law linking dynamic exponents.

Contribution

It introduces a novel scaling law $z=2+erb5\u03c7$ for the $O(2)$ model, connecting length scales and dynamics in systems with topological textures.

Findings

Derived the scaling law $z=2+erb5$ for the model.

Revealed the relationship between phase coherence and winding lengths.

Provided a simple scaling description of defect density evolution.

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, $L_{w} \sim L^{\chi}$. We derive the scaling law $z=2+\mu\chi$, where $\mu=0$ ($\mu=2$) for nonconserved (conserved) dynamics and $\chi=1/2$ 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)