Complex phase-ordering of the one-dimensional Heisenberg model with conserved order parameter

TL;DR

This paper investigates the phase-ordering dynamics of a one-dimensional Heisenberg model with conserved order parameter, revealing complex coexisting regimes with distinct growth laws and breaking traditional scaling assumptions.

Contribution

It introduces a detailed analysis of the coexisting length scales and their growth laws, providing new insights into the non-trivial ordering mechanisms.

Findings

Identification of two distinct growing lengths during phase ordering.

Observation of different growth laws: L_V(t) ~ t^{1/3} and L_C(t) ~ t^{1/4}.

Violation of dynamical scaling due to coexisting ordering mechanisms.

Abstract

We study the phase-ordering kinetics of the one-dimensional Heisenberg model with conserved order parameter, by means of scaling arguments and numerical simulations. We find a rich dynamical pattern with a regime characterized by two distinct growing lengths. Spins are found to be coplanar over regions of a typical size $L_V(t)$, while inside these regions smooth rotations associated to a smaller length $L_C(t)$ are observed. Two different and coexisting ordering mechanisms are associated to these lengths, leading to different growth laws $L_V(t)\sim t^{1/3}$ and $L_C(t)\sim t^{1/4}$ violating dynamical scaling.