Computer studies of spin and energy transport in one-dimensional Heisenberg magnets

Abstract

We have studied the dynamics of the classical Heisenberg chain at finite and infinite temperatures by computer simulation of an array of 4000 spins. The evaluation of the spin-spin and energy-energy wave-vector- and time-dependent correlation functions out to time $10J^{-1\mathrm{}}$ made it possible to determine the spin and energy diffusion constants. At infinite temperature we find $D_S=(1.33\mathrm{}\pm 0.10)JS{a}^2$ and $D_E=(3\mathrm{}\pm 1)JS{a}^2$. Values of $D_S$ have also been determined, with less precision, for ferromagnetic and antiferromagnetic interactions at temperatures $\frac{k_{B}T}{\mathrm{}\left|J\right|\mathrm{}}=1.0\mathrm{} \mathrm{and} 0.5$. Our results are compared with various theoretical estimates. In addition, we calculate the time-dependent spin and energy self-correlation functions.