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

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 $1/2\ge a{T}_c\ge 1/6$. Similar behaviour is found for the potential measured in a fixed physical volume.

28 pages (latex) + 11 figures (Postscript), uuencoded

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