Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow

Abstract

The energy density and the pressure of SU(3) gauge theory at finite temperature are studied by direct lattice measurements of the renormalized energy-momentum tensor obtained by the gradient flow. Numerical analyses are carried out with $\beta =6.287$--$7.500$ corresponding to the lattice spacing $a=0.013$--$0.061\mathrm{fm}$. The spatial (temporal) sizes are chosen to be $N_s=64$, $96$, $128$ ($N_{\tau }=12$, $16$, $20$, $22$, $24$) with the aspect ratio, $5.33\le N_s/N_{\tau }\le 8$. Double extrapolation, $a\to 0$ (the continuum limit) followed by $t\to 0$ (the zero flow-time limit), is taken using the numerical data. Above the critical temperature, the thermodynamic quantities are obtained with a few percent precision including statistical and systematic errors. The results are in good agreement with previous high-precision data obtained by using the integral method.

Comments: 12pages, many figures