Kosterlitz-Thouless theory and lattice artifacts

The massive continuum limit of the 1+1 dimensional O(2) nonlinear $\sigma$-model (XY model) is studied using its equivalence to the Sine-Gordon model at its asymptotically free point. It is shown that leading lattice artifacts are universal but they vanish only as inverse powers of the logarithm of the correlation length. Such leading artifacts are calculated for the case of the scattering phase shifts and the correlation function of the Noether current using the bootstrap S-matrix and perturbation theory respectively.