Surface properties at the Kosterlitz–Thouless transition

Abstract

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( T KT)=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 η 1( T KT)≃0.54.