Equation of State for the SU(3) Gauge Theory

TL;DR

This paper investigates the thermodynamic properties of the SU(3) gauge theory at finite temperature using lattice simulations, providing continuum extrapolated results for pressure, energy density, and critical temperature, revealing deviations from ideal gas behavior.

Contribution

It presents a detailed lattice study of the SU(3) gauge theory's equation of state with continuum extrapolation, improving understanding of non-ideal behavior at high temperatures.

Findings

Deviation from ideal gas behavior of 15-20% at high temperatures

Continuum limit estimate of T_c/√σ = 0.629(3)

Finite lattice effects controlled through multiple lattice sizes

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 $T_c/\sqrt{\sigma} = 0.629(3)$.