Topological charge and cooling scales in pure SU(2) lattice gauge theory

TL;DR

This study uses Monte Carlo simulations to analyze topological charges and cooling scales in pure SU(2) lattice gauge theory, providing continuum estimates of topological susceptibility and examining sector differences.

Contribution

It introduces improved reliability of topological charge measurements at higher $eta$ and lattice sizes, and offers continuum estimates of the topological susceptibility in SU(2).

Findings

Topological charges become more reliable with higher $eta$ and larger lattices.

Estimated topological susceptibility $ imes$ 1/4 is approximately 0.643.

Differences in cooling length scales across topological sectors are statistically insignificant.

Abstract

Using Monte Carlo simulations with overrelaxation, we have equilibrated lattices up to $\beta=2.928$, size $60^4$, for pure SU(2) lattice gauge theory with the Wilson action. We calculate topological charges with the standard cooling method and find that they become more reliable with increasing $\beta$ values and lattice sizes. Continuum limit estimates of the topological susceptibility $\chi$ are obtained of which we favor $\chi^{1/4}/T_c=0.643\,(12)$, where $T_c$ is the SU(2) deconfinement temperature. Differences between cooling length scales in different topological sectors turn out to be too small to be detectable within our statistical errors.