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

TL;DR

This paper introduces a new estimator for the correlation function in 2D nonlinear sigma models, significantly reducing statistical errors and enabling more precise measurements of the running coupling in these models.

Contribution

A novel improved estimator for correlation functions in 2D nonlinear sigma models, outperforming previous methods in reducing statistical errors.

Findings

Error reduction by up to a factor of 30 in small volumes

Enhanced accuracy in determining the running coupling

Effective for 2D XY and O(3) models

Abstract

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 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. L"uscher et al. for 2D O(N)-invariant vector models.