Equation of State for the SU(3) Gauge Theory

G. Boyd, J. Engels, F. Karsch, E. Laermann, C. Legeland, M. Lütgemeier, B. Petersson
1995 Physical Review Letters  
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,
more » ... ng 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 $T_c/\sqrt{\sigma} = 0.629(3)$.
doi:10.1103/physrevlett.75.4169 pmid:10059837 fatcat:n5kjjgaoizatjl67i2vab6f3x4