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

TL;DR

This paper addresses the equation of state for pure SU(3) gauge theory using a renormalization-group (RG)–improved action and tests continuum extrapolation against the standard plaquette action. It employs the integral method on lattices $N_t=4$ and $N_t=8$ with scale setting via the string tension to extract $p$ and $\epsilon$ and to determine $T_c$ and the continuum EOS. The main finding is that, after continuum extrapolation, the RG-improved EOS agrees with the plaquette-action results within $3$–$4\%$, validating action-independence of the continuum limit, though finite-$N_t$ effects and perturbative-limit behavior show nontrivial deviations. Comparisons with the operator method suggest nonperturbative contributions at accessible lattice spacings, highlighting the need for further study of high-temperature behavior in lattice QCD thermodynamics.

Abstract

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 $16^3\times 4$ and a $32^3\times 8$ 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%.

Figures (10)

• Figure 1: Bin size dependence of the jack-knife error of the action density
• Figure 2: String tension as a function of gauge coupling. Solid line represents a fit to Allton's parametrization.
• Figure 3: $T_c/\sqrt{\sigma}$ as a function of $1/N_t^2$. Open circles are results reported in Ref. ourPot97. Open squares are values for the plaquette actionBeinlich.
• Figure 4: Action difference $\Delta S$ for $N_t = 4$ and $8$ as a function of $\beta$.
• Figure 5: Pressure for $N_t = 4$ and 8. The dashed horizontal line on the top-right represents the leading order perturbative value in the high temperature limit in the continuum, and solid and dotted lines are the corresponding lattice values for $N_t =8$ and 4.