Asymptotic scaling and continuum limit of pure SU(3) lattice gauge theory

TL;DR

This paper demonstrates that the behavior of pure SU(3) lattice gauge theory across a broad range of couplings can be accurately described by asymptotic scaling formulas, providing insights into continuum limits and systematic errors.

Contribution

It shows that the entire range of couplings from 5.7 to 7.5 is well described by asymptotic scaling using 2-loop and 3-loop approximations, linking gradient flow and deconfinement observables.

Findings

Asymptotic scaling describes the data across the studied range.

Identical ratios for gradient flows and deconfinement observables are found.

Normalization constants reveal systematic errors.

Abstract

Recently the Yang-Mills gradient flow of pure SU(3) lattice gauge theory has been calculated in the range from $\beta=6/g_0^2=6.3$ to~7.5 (Asakawa et al.), where $g_0^2$ is the bare coupling constant of the SU(3) Wilson action. Estimates of the deconfining phase transition are available from $\beta =5.7$ to~6.8 (Francis et al.). Here it is shown that the entire range from 5.7 to 7.5 is well described by a power series of the lattice spacing $a$ times the lambda lattice mass scale $\Lambda_L$, using asymptotic scaling in the 2-loop and 3-loop approximations for $a\Lambda_L$. In both cases identical ratios for gradient flows versus deconfinement observables are obtained. Differences in the normalization constants with respect to $\Lambda_L$ give a handle on their systematic errors.