  We study the classical XY (plane rotator) model at the Kosterlitz-Thouless
phase transition. We simulate the model using the single cluster algorithm on
square lattices of a linear size up to L=2048.We derive the finite size
behaviour of the second moment correlation length over the lattice size
xi_{2nd}/L at the transition temperature. This new prediction and the analogous
one for the helicity modulus are confronted with our Monte Carlo data. This way
beta_{KT}=1.1199 is confirmed as inverse transition temperature. Finally we
address the puzzle of logarithmic corrections of the magnetic susceptibility
chi at the transition temperature.
