Deconfinement, gradient and cooling scales for pure SU(2) lattice gauge theory

TL;DR

This paper compares different scale-setting methods in pure SU(2) lattice gauge theory, demonstrating that gradient and cooling flows significantly improve computational efficiency while maintaining accuracy in approaching the continuum limit.

Contribution

It introduces and evaluates the efficiency of gradient and cooling flow methods for scale setting, showing they outperform traditional deconfinement scales in SU(2) lattice gauge theory.

Findings

Gradient flow is at least 100 times more efficient than deconfinement scale.

Cooling flow is at least 34 times more efficient than gradient flow.

Wilson action performs as well or better than other observables for scale setting.

Abstract

We investigate the approach of pure SU(2) lattice gauge theory with the Wilson action to its continuum limit using the deconfining phase transition, the gradient flow and the cooling flow to set the scale. For the gradient and cooling scales we explore three different energy observables and two distinct reference values for the flow time. When the aim is to follow scaling towards the continuum limit, one gains at least a factor of 100 in computational efficiency by relying on the gradient instead of the deconfinement scale. Using cooling instead of the gradient flow one gains another factor of at least 34 in computational efficiency on the gradient flow part without any significant loss in the accuracy of scale setting. Concerning our observables, the message is to keep it simple. The Wilson action itself performs as well as or even better than the other two observables explored. Two distinct fitting forms for scaling are compared of which one connects to asymptotic scaling. Differences of the obtained estimates show that systematic errors of length ratios, though only about 1%, can be considerably larger than statistical errors of the same observables.