# Study of Critical Slowing-Down in $SU(2)$ Landau Gauge Fixing

## TL;DR

This paper investigates the phenomenon of critical slowing-down in gauge-fixing algorithms for $SU(2)$ lattice gauge theory, analyzing five algorithms across 2D and 4D lattices through numerical and analytical methods.

## Contribution

It provides a comparative analysis of five gauge-fixing algorithms and discusses their tuning, offering insights into their performance and behavior in $SU(2)$ Landau gauge fixing.

## Key findings

- Critical slowing-down observed in all algorithms.
- Performance varies significantly among the algorithms.
- Analytical and numerical results agree on the slowing-down behavior.

## Abstract

We study the problem of critical slowing-down for gauge-fixing algorithms (Landau gauge) in $SU(2)$ lattice gauge theory on $2$ and $4$ dimensional lattices, both numerically and analytically. We consider five such algorithms, and we measure four different observables. A detailed discussion and analysis of the tuning of these algorithms is also presented.