A simulation study of energy transport in the Hamiltonian XY model

The transport properties of the planar rotator model on a square lattice are analysed by means of microcanonical and non-equilibrium simulations. Well below the Kosterlitz-Thouless-Berezinskii transition temperature, both approaches consistently indicate that the energy current autocorrelation displays a long-time tail decaying as t-1. This yields a thermal conductivity coefficient which diverges logarithmically with the lattice size. Conversely, conductivity is found to be finite in the high-temperature disordered phase. Simulations close to the transition temperature are instead limited by slow convergence that is presumably due to the slow kinetics of vortex pairs.