Scaling Violations with Textures in Two-Dimensional Phase-Ordering

TL;DR

This paper investigates scaling violations in the two-dimensional Heisenberg model with textures, revealing multiple length-scales that challenge traditional scaling assumptions in phase-ordering dynamics.

Contribution

It identifies and characterizes three distinct length-scales in the Heisenberg model, highlighting the presence of scaling violations due to topological textures.

Findings

Three length-scales: $L_T$, $L_N$, $L_C$

Scaling violations observed in the model

Textures influence phase-ordering dynamics

Abstract

Scaling violations are found in the phase-ordering two-dimensional Heisenberg [$O(3)$] model, which has non-singular topological textures, under dissipative non-conserved dynamics. Three separate length-scales are found: $L_T$ characterizes the scale of individual textures, $L_N$ characterizes the separation between textures, and $L_C$ characterizes the distance between oppositely charged textures.