A simulation study of energy transport in the Hamiltonian XY-model

TL;DR

This study investigates energy transport in the XY-model, revealing divergent thermal conductivity at low temperatures and finite conductivity at high temperatures through simulation analysis.

Contribution

It provides the first detailed simulation analysis of energy transport in the XY-model across different temperature regimes.

Findings

Long-time tail in energy current autocorrelation at low temperatures

Logarithmic divergence of thermal conductivity with system size at low temperatures

Finite thermal conductivity in the high-temperature disordered phase

Abstract

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.