The transport properties of the planar rotator model on a square lattice are
analyzed 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 insted
limited by slow convergence that is presumably due to the slow kinetics of
vortex pairs.Comment: Submitted to Journal of Statistical Mechanics: theory and experimen