Fractal Dimension of Gauge-fixing Defects

Abstract

The fractal dimension $D_f$ of sites resisting Landau or maximal Abelian(MA) gauge fixing in lattice $SU(3)$ gluodynamics is defined and computed. In Landau gauge such sites clump into $D_f\sim 1$ clusters in the confining phase. In the finite temperature phase their dimensionality drops to $D_f<1$, that is, clustering seems to dissipate. In contrast, MA gauge resistant sites fail to exhibit a notable tendency to cluster at any temperature.

Comments: 12 pages (A page of additional discussion has been inserted into the original version. This is the final version accepted for publication.)