Equation of State for the SU(3) Gauge Theory

Abstract

Through a detailed investigation of the $SU(3)$ gauge theory at finite temperature on lattices of various size we can control finite lattice cut-off effects in bulk thermodynamic quantities. We calculate the pressure and energy density of the $SU(3)$ gauge theory on lattices with temporal extent $N_{\tau }=4$, 6 and 8 and spatial extent $N_{\sigma }=16$ and 32. The results are extrapolated to the continuum limit. We find a deviation from ideal gas behaviour of (15-20)\%, depending on the quantity, even at temperatures as high as $T\sim 3T_c$. A calculation of the critical temperature on lattices with temporal extent $N_{\tau }=8$ and 12 and the string tension on $32^4$ lattices at the corresponding critical couplings is performed to fix the temperature scale. An extrapolation to the continuum limit yields $T_c/\sqrt{\sigma }=0.629(3)$.

Comments: 12 pages, LaTeX2e, 5 figures in a seperate uuencoded compressed file. fixed end{document}