Scaling of the critical temperature and the quark potential with a renormalization group improved SU ( 3 ) gauge action ∗

We study the scaling property of the ratio of the critical temperature Tc to the square root of the string tension σ in the SU(3) pure gauge theory using a renormalization group (RG) improved action. We first determine the critical coupling βc on lattices with temporal extension Nt = 4 and 6, and then calculate the static quark potential at the critical couplings on lattices at zero temperature. The values of Tc/ √ σ in the infinite volume limit are identical within errors, while they are slightly larger than the value extrapolated to the continuum limit with the standard action. We also note that the rotational invariance of the static quark potential is remarkably restored in the both cases, and that the potential V (R) in physical units scales in the whole region of R investigated.