Critical Slowing-Down in $SU(2)$ Landau Gauge-Fixing Algorithms

Details Critical Slowing-Down in $SU(2)$ Landau Gauge-Fixing Algorithms Critical Slowing-Down in $SU(2)$ Landau Gauge-Fixing Algorithms

1995-11-19

arxiv.org/abs/hep-lat/9511020v2

Nucl.Phys. B471 (1996) 263-292

Physics

High Energy Physics

High Energy Physics - Lattice

40 pages (including 10 figures). A few modifications, incorporating referee's suggestions, without the length reduction requir

Scientific paper

10.1016/0550-3213(96)00177-0

We study the problem of critical slowing-down for gauge-fixing algorithms (Landau gauge) in $SU(2)$ lattice gauge theory on a $2$-dimensional lattice. We consider five such algorithms, and lattice sizes ranging from $8^{2}$ to $36^{2}$ (up to $64^2$ in the case of Fourier acceleration). We measure four different observables and we find that for each given algorithm they all have the same relaxation time within error bars. We obtain that: the so-called {\em Los Alamos} method has dynamic critical exponent $z \approx 2$, the {\em overrelaxation} method and the {\em stochastic overrelaxation} method have $z \approx 1$, the so-called {\em Cornell} method has $z$ slightly smaller than $1$ and the {\em Fourier acceleration} method completely eliminates critical slowing-down. A detailed discussion and analysis of the tuning of these algorithms is also presented.

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