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Physica A Statistical Mechanics and its Applications

Two-spin dynamic autocorrelations and energy diffusion in the Heisenberg paramagnet

Michel De Leener, Pierre M. V. Résibois

Published Apr 1, 1977• 1 citation
Publisher
DOI
10.1016/0378-4371(77)90168-6

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The energy and spin diffusion behaviors in the one-dimensional classical Heisenberg spin chain have been systematically investigated using the equilibrium diffusion method. The spatiotemporal autocorrelation functions for energy and spin are calculated at finite and infinite temperatures. As conserved quantities, the spreading of excess energy and spin can be used to determine their actual diffusion behaviors. At low temperatures, the energy diffusion shows almost ballistic behavior, and spin shows superdiffusion behavior for finite chain size. For energy diffusion, normal diffusion behavior can be obtained when the temperature is higher than 0.75. For spin diffusion, normal diffusion behavior is observed at infinite temperature.
The problem of spin diffusion is studied numerically in the one-dimensional classical Heisenberg model using a deterministic odd-even spin precession dynamics. We demonstrate that spin diffusion in this model is normal in the infinite-temperature limit and one obtains a long-time diffusive tail in the decay of the autocorrelation function. Some variations of the model with different coupling schemes and anisotropy are also studied and we find normal diffusion in all of them. A systematic finite-size analysis also suggests normal diffusive spreading of spin fluctuations, contrary to previous claims of anomalous diffusion. We also briefly discuss spin diffusion in this model at finite temperatures.