Non--perturbative tests of the fixed point action for SU(3) gauge theory

TL;DR

This paper extends the calculation of a classical fixed point action for SU(3) lattice gauge theory to include large fluctuations, demonstrating improved scaling behavior over Wilson action in lattice simulations.

Contribution

It introduces a few-parameter approximation to the fixed point action valid for short correlation lengths and tests its scaling properties in lattice gauge theory.

Findings

Fixed point action scales within errors for 1/2 ≥ aT_c ≥ 1/6

Wilson action shows about 10% scaling violations

Potential measurements confirm improved scaling behavior

Abstract

In this paper (the second of a series) we extend our calculation of a classical fixed point action for lattice $SU(3)$ pure gauge theory to include gauge configurations with large fluctuations. The action is parameterized in terms of closed loops of link variables. We construct a few-parameter approximation to the classical FP action which is valid for short correlation lengths. We perform a scaling test of the action by computing the quantity $G = L \sqrt{\sigma(L)}$ where the string tension $\sigma(L)$ is measured from the torelon mass $\mu = L \sigma(L)$. We measure $G$ on lattices of fixed physical volume and varying lattice spacing $a$ (which we define through the deconfinement temperature). While the Wilson action shows scaling violations of about ten per cent, the approximate fixed point action scales within the statistical errors for $ 1/2 \ge aT_c \ge 1/6$. Similar behaviour is found for the potential measured in a fixed physical volume.