Heat diffusion in a classical Heisenberg chain

We study the heat transport in a one dimensional classical Heisenberg chain by means of spin dynamics simulation. The system consists of a $N=2000$ spins in the microcanonical ensemble, and the temperature is evaluated using the so-called configurational temperature formula. We thermalize the system to an equilibrium state at low temperature, and then we give a delta function energy packet in the middle of the chain. Studying both qualitatively and quantitatively the spreading of the delta, we characterize the diffusion of heat in the chain. In fact, calculating the second moment of the pulse, and using the relation \begin{equation} \left\langle \sigma (t) ^2\right\rangle =2 D t^{\alpha}, \,~ ( 0 < \alpha < 2), \end{equation} where $\sigma$ is the width of the pulse, $D$ is the diffusion constant and $\alpha$ is a parameter which consider the kind of diffusion. According our simulation, the heat in this system transports subdiffusively. This result imply that the system becomes a thermal insulator in the thermodynamic limit $N \rightarrow \infty $.