Classically perfect gauge actions on anisotropic lattices

We present a method for constructing classically perfect anisotropic action s for SU(3) gauge theory based on an isotropic Fixed Point Action. The acti on is parametrised using smeared ("fat") links. The construction is done ex plicitly for anisotropy xi a(s)/a(t) = 2 and 4. The corresponding renormali sed anisotropies are determined using the torelon dispersion relation. The renormalisation of the anisotropy is small and the parametrisation describe s the true action well. Quantities such as the static quark-antiquark poten tial, the critical temperature of the deconfining phase transition and the low-lying glueball spectrum are measured on lattices with anisotropy = 2. T he mass of the scalar 0(++) glueball is determined to be 1580(60) MeV, whil e the tensor 2(++) glueball is at 2430(60) Mev. (C) 2001 Published by Elsev ier Science B.V.