Center vortices in MCG - finite-size and gauge-copy effects

TL;DR

This study examines how lattice size and gauge-copy choices affect vortex detection and string tension measurements in SU(2) lattice gauge theory, confirming the stability of vortex-related observables on large lattices.

Contribution

It provides a detailed analysis of finite-size and gauge-copy effects on vortex observables, demonstrating their diminishing impact on sufficiently large lattices.

Findings

Dependence on gauge copies decreases with larger lattices.

Center-projected string tension matches full string tension on large lattices.

Vortex density scales according to asymptotic freedom formula.

Abstract

In SU(2) lattice gauge theory in maximal center gauge, we investigate the dependence of center-projected Creutz ratios and the vortex density on lattice size and the number of gauge copies. The dependence on the number of copies is rather strong on small lattices, but almost disappears on lattices sufficiently large compared to the expected average vortex thickness. The center-projected string tension, evaluated on sufficiently large lattices, is in good agreement with the full asymptotic string tension, and the vortex density scales according to the second-order asymptotic-freedom formula.