Influence of quenched dilution on the quasi-long-range ordered phase of the <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\mathsf{2d}$</EquationSource> </InlineEquation> <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\mathsf{XY}$</EquationSource> </InlineEquation> model

The influence of non magnetic impurities in the 2d XY model is investigated through Monte Carlo (MC) simulations. The general picture of the transition is fully understood from the Harris criterion which predicts that the universality class is unchanged, and the Berezinskii-Kosterlitz-Thouless description of the topological transition remains valid. We nevertheless address here the question about the influence of dilution on the quasi-long-range order at low temperatures. In particular, we study the asymptotic of the pair correlation function and report the MC estimates for the critical exponent <InlineEquation ID="Equ3"> <EquationSource Format="TEX">$\eta$</EquationSource> </InlineEquation> at different dilutions. In the weak dilution region, our MC calculations are further supported by simple spin-wave-like calculations. Copyright Springer-Verlag Berlin/Heidelberg 2003