Groupe de Physique Statistique

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 ηâ^¥ 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) âo/oof 0.54.