Bounding statistical errors in lattice field theory simulations

TL;DR

This paper proposes a new automatic windowing method for estimating statistical errors in lattice field theory simulations, accounting for autocorrelations more effectively.

Contribution

It introduces a stopping criterion based on bounds of the autocorrelation function and applies it to traditional and master-field Monte Carlo methods.

Findings

The new method improves error estimation accuracy.

The approach is validated on simplified toy models.

It enhances the reliability of autocorrelation analysis in simulations.

Abstract

Simulations of strongly interacting lattice field theories are typically performed using Markov chain Monte Carlo algorithms. Therefore estimators of statistical errors must incorporate the effect of autocorrelations by integrating the corresponding autocorrelation function. Since in practical calculations its integral is truncated to a finite window, in this work we propose a stopping criterion based on upper and lower bounds of the autocorrelation function. We examine its application to both traditional Monte Carlo analysis and the recently introduced master-field approach. By leveraging both bounds, we introduce an automatic windowing procedure which we test on numerical simulations of a few simplified toy models.