Critical slowing-down in SU(2) Landau gauge-fixing algorithms Original Research Article

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 82 to 362 (up to 642 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 Los Alamos method has a dynamic critical exponent z ≈ 2, the overrelaxation method and the stochastic overrelaxation method have z ≈ 1, the so-called Cornell method has z slightly smaller than 1 and the Fourier acceleration method completely eliminates critical slowing-down. A detailed discussion and analysis of the tuning of these algorithms is also presented.