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

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.