A precise study of the SU(3) Yang-Mills theory across the deconfinement transition

TL;DR

This paper provides a detailed lattice computation of the deconfinement transition in SU(3) Yang-Mills theory, accurately determining the critical temperature, latent heat, and equation of state across the phase transition.

Contribution

It offers the first precise continuum-limit calculations of entropy density, latent heat, and critical temperature across the deconfinement transition in SU(3) Yang-Mills theory.

Findings

Latent heat measured as discontinuity in trace anomaly: h=1.175(10)

Critical temperature determined with permille accuracy: T_c√t_0=0.24915(29)

Equation of State computed for temperatures up to 3.4 T_c

Abstract

We perform a detailed computation of key quantities across the first-order deconfinement phase transition of the SU(3) Yang-Mills theory. Specifically, we calculate the entropy density, $s(T_c)/T_c^3$, on both sides of the transition and determine the latent heat $h$. The calculations are carried out in the lattice regularization with the Wilson action, employing shifted boundary conditions in the temporal direction. Our simulations are performed at five different values of the lattice spacing in order to extrapolate the results to the continuum limit. The latent heat can be measured also as the discontinuity in the trace anomaly of the energy-momentum tensor: our result using the entropy density is compatible with the one obtained from the trace anomaly, giving a combined estimate $h=1.175(10)$. Additionally, we determine the critical temperature $T_c$ in physical units with permille accuracy, yielding $T_c \sqrt{t_0} = 0.24915(29)$. These results allow to connect with precision the confined and the deconfined phases and we present an improved computation of the Equation of State across the deconfinement transition for $T$ between 0 and $3.4 T_c$.