# Thermodynamics of SU(3) Lattice Gauge Theory

## TL;DR

This paper calculates thermodynamic properties of SU(3) gauge theory on the lattice, explores continuum extrapolation, and investigates the behavior of the running coupling and string tension at high temperatures.

## Contribution

It provides new continuum limit results for pressure, energy density, critical temperature, and string tension in SU(3) lattice gauge theory, including temperature dependence of various condensates.

## Key findings

- 15% deviation from ideal gas at high T
- Critical temperature ratio T_c/√σ = 0.629(3)
- Running coupling remains large up to 5T_c

## Abstract

The pressure and the energy density of the $SU(3)$ gauge theory are calculated on lattices with temporal extent $N_\tau = 4$, 6 and 8 and spatial extent $N_\sigma =16$ and 32. The results are then extrapolated to the continuum limit. In the investigated temperature range up to five times $T_c$ we observe a $15\%$ deviation from the ideal gas limit. We also present new results for the critical temperature on lattices with temporal extent $N_\tau = 8$ and 12. At the corresponding critical couplings the string tension is calculated on $32^4$ lattices to fix the temperature scale. An extrapolation to the continuum limit yields $T_c/\sqrt{\sigma} = 0.629(3)$. We furthermore present results on the electric and magnetic condensates as well as the temperature dependence of the spatial string tension. These observables suggest that the temperature dependent running coupling remains large even at $T\simeq 5T_c$. For the spatial string tension we find $\sqrt{\sigma_s}/T = 0.566(13) g^2(T)$ with $g^2(5T_c) \simeq 1.5$.