Temperature in magnetic systems: Evolution towards thermal equilibrium by spin dynamics simulation

The concept of temperature in magnetic systems is examined by studying how two spin systems in thermal contact reach equilibrium. Using the spin dynamics simulation method, we consider two planar arrays of classical spins governed by the Heisenberg Hamiltonian, interacting with each other through an edge. According to an expression for the temperature of the system based solely on spin configurational degrees of freedom, we are able to obtain the temperature evolution with respect to time. The spin temperature follows an exponential behavior, and can be modeled by the Newton cooling law, reaching a common final temperature which is in complete agreement with the theoretical thermodynamic prediction. The simulation results give new insight on the meaning of temperature for magnetic systems and provide an operational method to calculate it in computer simulation.