Surface properties at the Kosterlitz-Thouless transition

Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with free and mixed fixed-free boundary conditions. Using a Schwarz-Christoffel conformal mapping, we deduce the exponent η of the order parameter correlation function and its surface equivalent η‖ at the Kosterlitz-Thouless transition temperature. The well known value η(TKT) = 1/4 is easily recovered even with systems of relatively small sizes, since the shape effects are encoded in the conformal mapping. The exponent associated to the surface correlations is similarly obtained η1(TKT) ≃ 0.54.