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

Source: [Complex phase-ordering of the one-dimensional Heisenberg model with conserved order parameter](<https://www.sota2.com/research/paper/68fa23942c2a376019399ace>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:52:35.152Z

Authors: R. Burioni, F.Corberi, A. Vezzani

Published: 2009-03-26T12:58:12.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0903.4564>)

[PDF](<https://arxiv.org/pdf/0903.4564.pdf>)