Thermally driven classical Heisenberg model in one dimension

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.

9 pages, 13 eps figures

References in corpus (5)

• Heat Transport in low-dimensional systems
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Heat conduction in low-dimensional quantum magnets
• Thermal conductivity via magnetic excitations in spin-chain materials
• Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories

Cited by in corpus (5)

• Spin diffusion in one-dimensional classical Heisenberg mode
• Thermal Rectification and Negative Differential Thermal Resistance in a driven two segment classical Heisenberg chain
• Thermally driven classical Heisenberg chain with a spatially varying magnetic field: Thermal rectification and Negative differential thermal resistance
• A microscopic model of ballistic-diffusive crossover
• Thermally driven classical Heisenberg model in one dimension with a local time-varying field