Equation of State for the SU(3) Gauge Theory

By investigating the SU(3) gauge theory thermodynamics on lattices of various sizes we can control finite lattice cutoff effects. We calculate the pressure and energy density on lattices with temporal extent $N_{\tau }=4, 6, \mathrm{and} 8$ and spatial extent $N_{\sigma }=16\mathrm{} \mathrm{and} 32$, and extrapolate to the continuum limit. We find a deviation from ideal gas behavior of (15-20)%, even at temperatures as high as $T\sim 3T_c$. A calculation of the critical temperature for $N_{\tau }=8\mathrm{} \mathrm{and} 12$ and the string tension for $N_{\tau }=32\mathrm{}$ is performed to fix the temperature scale, yielding $\frac{T_c}{\sqrt{\sigma }}=0.629\mathrm{}\left(3\right)\mathrm{}$ in the continuum limit.