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Séminaire CETHIL -Temperature in magnetic systems: evolution towards thermal equilibrium by spin dynamics simulation

Le 17 avril 2019

Amphi Claude Chappe, INSA

Présenté par : Gonzalo Gutiérrez, Departamento de Física, Facultad de Ciencias, Universidad de Chile

We present an equipartion–like formula for classical spin systems which in useful in computer simulation to “measure” the temperature of magnetic systems by taking time average over spin configurations. Such temperature estimator is independent of the ensemble, an allows us to monitor the temperature in spin dynamics simulation, as well as to gain a deeper understanding of the meaning of temperature. We illustrate the usefulness of this formula in two cases. Firstly, in
order to check our procedure, we consider two planar arrays of classical spins governed by the Heisenberg hamiltonian, interacting each other through an edge.

We follow the temperature evolution with respect to time, finding an exponential behavior to equilibrium, like Newton cooling law, reaching a common final temperature which is in complete agreement with the theoretical thermodynamic prediction. Secondly, we use the temperature estimator to study the heat diffusion in a Heisenberg chain. 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, and following the temperature evolution, we can gain insight about the diffusion of heat in the chain.