  We study the two dimensional XY-model with high precision Monte Carlo
techniques and investigate the continuum approach of the step-scaling function
of its finite volume mass gap. The continuum extrapolated results are found
consistent with analytic predictions for the finite volume energy spectrum
based on the equivalence with sine-Gordon theory. To come to this conclusion it
was essential to use an also predicted form of logarithmic decay of lattice
artifacts for the extrapolation.
