Equation of state for pure SU(3) gauge theory with renormalization group improved action

A lattice study of the equation of state for pure SU~3! gauge theory using a renormalization-group ~RG! improved action is presented. The energy density and pressure are calculated on a 16 3 3 4a nd a3 2 3 38 lattice employing the integral method. Extrapolating the results to the continuum limit, we find the energy density and pressure to be in good agreement with those obtained with the standard plaquette action within the error of 3-4 %.@S0556-2821~99!07819-4# In this article we report on our study of the continuum limit of the equation of state for pure SU~3! gauge theory with an improved action determined from an approximate renormalization-group argument @7#. Simulations are carried out on 16 3 34 and 32 3 38 lattices, and the energy density and pressure are calculated by the integral method @8# .W e find that the results extrapolated to the continuum limit agree well with those obtained from the standard action in Ref. @2#. This provides us with a crosscheck of the final results in the continuum limit, and also provide support for the validity of assumptions behind the extrapolation procedures. This paper is organized as follows. In Sec. II, we summa- rize the basic formulation and our notations. Some details of our simulations are given in Sec. III. We define our choice of the temperature scale in terms of the string tension in Sec. IV, and examine scaling of the critical temperature in Sec. V. In Sec. VI we present our results for equation of state ob- tained at Nt54 and 8, and their continuum extrapolation. A comparison of our results with those obtained from the stan- dard action is also made. In Sec. VII we briefly discuss re- sults obtained with the operator method @9#. We end with a brief conclusion in Sec. VIII.