Anomalous Spin Diffusion in Classical Heisenberg Magnets

Time-dependent spin-autocorrelation functions at $T=\infty$ for classical Heisenberg magnets in dimensionalities $d=1, 2, \mathrm{and} 3$ are investigated by means of a computer simulation. These functions are shown to exhibit power-law long-time tails of form $t^{-{\alpha }_d}$ with characteristic exponents ${\alpha }_d$ which differ significantly from the values ${\alpha }_d^{\mathrm{}\left(\mathrm{SD}\right)\mathrm{}}=\frac{d}{2}$ predicted by the phenomenological spin-diffusion theory: ${\alpha }_1=0.609\mathrm{}\pm 0.005$, ${\alpha }_2=1.050\mathrm{}\pm 0.025$, ${\alpha }_3\simeq 1.6$. The method to employ computer simulations for this problem differs from methods previously employed. Anomalous spin diffusion is confirmed by existing proton spin-lattice relaxation data for the quasi-1D $s=\frac{5}{2}$ Heisenberg antiferromagnet ${\left(\mathrm{C}{\mathrm{H}}_3\right)}_4$NMn${\mathrm{Cl}}_3$.