An Improved Estimator for the Correlation Function of 2D Nonlinear Sigma Models

I present a new improved estimator for the correlation function of 2D nonlinear sigma models. Numerical tests for the 2D XY model and the 2D O(3)-invariant vector model were performed. For small physical volume, i.e. a lattice size small compared to the bulk correlation length, a reduction of the statistical error of the finite system correlation length by a factor of up to 30 compared to the cluster-improved estimator was observed. This improvement allows for a very accurate determination of the running coupling proposed by M. Lüscher et al. for 2D O(N)invariant vector models. CERN-TH.7375/94 August 1994 1 Address after September 30, 1994: DAMTP, Silver Street, Cambridge, CB3 9EW, England