Debarshee Bagchi, P. K. Mohanty
We study thermal transport in classical one dimensional Heisenberg model employing a discrete time odd even precessional update scheme. This dynamics equilibrates a spin chain for any arbitrary temperature and finite value of the integration time-step $\Delta t$. We rigorously show that in presence of driving the system attains local thermal equilibrium which is a strict requirement of Fourier law. In the thermodynamic limit heat current for such a system obeys Fourier law for all temperatures, as has been recently shown [Phys. Rev. B 72, 140402(R)]. Finite systems, however, show an apparent ballistic transport which crosses over to a diffusive one as the system size is increased. We provide exact results for current and energy profiles in small and large $\Delta t$ limits.
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http://arxiv.org/abs/1206.2827
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