Measuring the Decorrelation Times of Fourier Modes in Simulations

TL;DR

This paper introduces a method to measure how quickly different Fourier modes decorrelate in simulations, revealing differences between local and non-local dynamics that could inform the development of more efficient algorithms.

Contribution

The paper presents a novel approach to quantify mode-specific decorrelation times in simulations, applied to the XY model with different dynamics.

Findings

Metropolis and Wolff dynamics show markedly different autocorrelation behaviors.

The method identifies decorrelation times for individual modes.

Insights may lead to the design of more efficient simulation algorithms.

Abstract

We describe a method to study the rate at which modes decorrelate in numerical simulations. We study the XY model updated with the Metropolis and Wolff dynamics respectively and compute the rate at which each eigenvector of the dynamics decorrelates. Our method allows us to identify the decorrelation time for each mode separately. We find that the autocorrelation function of the various modes is markedly different for the `local' Metropolis compared to the `non-local' Wolff dynamics. Equipped with this new insight, it may be possible to devise highly efficient algorithms.