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

20 pages, LaTeX + 2 ps figures, CERN-TH.7375/94

References in corpus (1)

• High Precision Renormalization Group Study of the Roughening Transition

Cited by in corpus (9)

• The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
• The puzzle of apparent linear lattice artifacts in the 2d non-linear sigma-model and Symanzik's solution
• Simulating the All-Order Strong Coupling Expansion III: O(N) sigma/loop models
• Non-trivial θ-Vacuum Effects in the 2-d O(3) Model
• Nonstandard Cutoff Effects in the Nonlinear Sigma Model
• Cutoff Effects in O(N) Nonlinear Sigma Models
• Tests of the continuum limit for the $SO(4)$ Principal Chiral Model and the prediction for $Ł_\MS$
• Numerical confirmation of analytic predictions for the finite volume mass gap of the XY-model
• Lattice artefacts and the running of the coupling constant