Date of Original Version
This computer simulation study provides further evidence that spin diffusion in the one‐dimensional classical Heisenberg model at T=∞ is anomalous: 〈S j ( t )⋅S j 〉 ∼t −α 1 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 〈S j ( t )⋅S j 〉 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.
Jian-Min Liu, Niraj Srivastava, V.S. Viswanath and Gerhard Müller. Deterministic and stochastic spin diffusion in classical Heisenberg magnets. J. Appl. Phys. 70 (1991), 6181-6183.
Available at: http://dx.doi.org/10.1063/1.350037