Spin diffusion in one-dimensional classical Heisenberg mode

TL;DR

This study numerically investigates spin diffusion in the one-dimensional classical Heisenberg model, demonstrating normal diffusion behavior and contrasting previous claims of anomalous diffusion.

Contribution

The paper provides the first systematic numerical evidence that spin diffusion in the 1D classical Heisenberg model is normal, including variations with anisotropy and different coupling schemes.

Findings

Spin diffusion is normal in the 1D classical Heisenberg model.

Autocorrelation functions exhibit long-time diffusive tails.

Finite size analysis supports diffusive spreading, contradicting earlier claims of anomalous diffusion.

Abstract

The problem of spin diffusion is studied numerically in one-dimensional classical Heisenberg model using a deterministic odd even spin precession dynamics. We demonstrate that spin diffusion in this model, like energy diffusion, is normal and one obtains a long time diffusive tail in the decay of autocorrelation function (ACF). Some variations of the model with different coupling schemes and with anisotropy are also studied and we find normal diffusion in all of them. A systematic finite size analysis of the Heisenberg model also suggests diffusive spreading of fluctuation, contrary to previous claims of anomalous diffusion.