P-Vortices, Gauge Copies, and Lattice Size

TL;DR

This paper investigates how lattice size and gauge copies affect the measurement of string tension in lattice gauge theory, showing that previous discrepancies are due to small lattice volumes and that larger lattices restore expected behavior.

Contribution

The study demonstrates that center dominance holds on larger lattices and clarifies the dependence of P-vortex properties on lattice size and gauge fixing procedures.

Findings

Center-projected string tension approaches full string tension on larger lattices.

P-vortex density follows 2-loop scaling at moderate couplings.

Previous breakdown of center dominance is due to small lattice sizes.

Abstract

We study the dependence of the center-projected string tension on both the lattice size, and the number of gauge copies used for maximal center gauge fixing. We show that a recent finding of Bornyakov, Komarov, Polikarpov, and Veselov (hep-lat/0002017), indicating a substantial breakdown of center dominance in maximal center gauge, is only obtained for rather small lattice volumes, and is not found in numerical simulations on larger lattices. It is shown that center-projected Creutz ratios approach the full asymptotic string tension as lattice size increases, and that the P-vortex density is consistent, at moderately weak couplings, with 2-loop scaling behavior.