Improved Langevin Methods for Spin Systems

TL;DR

This paper enhances Langevin methods for spin systems by reducing variance and systematic errors, demonstrating comparable efficiency to multi-grid methods in two-dimensional models.

Contribution

It introduces improved Langevin schemes that match multi-grid methods in accuracy and efficiency for certain spin models.

Findings

Results are consistent with multi-grid methods.

Langevin methods can be made competitive with multi-grid in terms of timing.

Variance reduction techniques improve the reliability of Langevin simulations.

Abstract

We investigate methods for variance reduction and the elimination of systematic error in a Fourier accelerated Langevin scheme for general spin models. We present results for the $SU(3)\times SU(3)/SU(3)$ model in two-dimensions that are consistent wit h those from multi-grid methods. We argue that the timing for the Langevin method makes it comparable to multi-grid for a given level of error.