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

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√ σ( L) where the string tension σ( L) is measured from the torelon mass μ = Lσ( 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} ⩾ aT _c ⩾ {1}/{6}. Similar behavior is found for the potential measured in a fixed physical volume.