Critical Slowing-Down in SU(2) Landau-Gauge-Fixing Algorithms at beta = infinity

TL;DR

This paper investigates the dynamic critical behavior of five gauge-fixing algorithms in SU(2) lattice Landau-gauge theory at infinite coupling, providing numerical and analytical insights into their efficiency and limitations across multiple dimensions.

Contribution

It offers the first comprehensive analysis of the dynamic critical exponent at infinite beta, clarifies algorithm tuning, and explores generalizations and gauge choices.

Findings

Numerical and analytical agreement on critical exponent z at infinite beta.

No local algorithm can achieve z less than 1.

Analytic results extend to lambda gauges, confirmed in 2D.

Abstract

We evaluate numerically and analytically the dynamic critical exponent $z$ for five gauge-fixing algorithms in SU(2) lattice Landau-gauge theory by considering the case $\beta = \infty$. Numerical data are obtained in two, three and four dimensions. Results are in agreement with those obtained previously at finite $\beta$ in two dimensions. The theoretical analysis, valid for any dimension $d$, helps us clarify the tuning of these algorithms. We also study generalizations of the overrelaxation algorithm and of the stochastic overrelaxation algorithm and verify that we cannot have a dynamic critical exponent $z$ smaller than 1 with these local algorithms. Finally, the analytic approach is applied to the so-called $\lambda$-gauges, again at $\beta = \infty$, and verified numerically for the two-dimensional case.