Breakdown of hydrodynamics in the classical 1D Heisenberg model

Extensive spin-dynamics simulations have been performed to study the dynamical behavior of the classical Heisenberg chain at infinite temperatures and long wavelengths. We find that the energy and spin show distinctly different dynamics in the isotropic system. The energy correlation function follows the classical diffusion theory prediction, namely, it decays exponentially with ${\mathit{q}}^2$t. In contrast, the spin correlation function is found to decay exponentially as ${\mathit{q}}^{2.12}$t lnt, implying a logarithmically divergent diffusion constant and the failure of the usual hydrodynamic assumptions.