Deterministic and stochastic spin diffusion in classical Heisenberg magnets

Abstract

This computer simulation study provides further evidence that spin diffusion in the one-dimensional classical Heisenberg model at T=∞ is anomalous: 〈Sj(t)⋅Sj〉 ∼t−α1 withα1 ≳1/2. However, the exponential instability of the numerically integrated phase-space trajectories transforms the deterministic transport of spin fluctuations into a computationally generated stochastic process in which the global conservation laws are still satisfied to high precision. This may cause a crossover in 〈Sj(t)⋅Sj〉 from anomalous spin diffusion (α1 ≳ 1/2) to normal spin diffusion (α1 = 1/2) at some characteristic time lag that depends on the precision of the numerical integration.