Thermally driven classical Heisenberg model in one dimension

TL;DR

This paper investigates thermal transport in a one-dimensional classical Heisenberg model using a discrete update scheme, demonstrating Fourier law compliance in the thermodynamic limit and analyzing finite-size effects.

Contribution

It provides a rigorous analysis of thermal transport and local equilibrium in a classical Heisenberg chain, including exact results at temperature extremes.

Findings

Fourier law holds in the thermodynamic limit for all temperatures.

Finite systems exhibit a crossover from ballistic to diffusive transport.

Exact energy and current profiles are derived at zero and infinite temperatures.

Abstract

We study thermal transport in a 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 [A. V. Savin, G. P. Tsironis, and X. Zotos, Phys. Rev. B 72, 140402(R) (2005)]. 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 zero- and infinite-temperature limits.