Parallel tempering algorithm applied to the deconfinement transition of quenched QCD

TL;DR

This paper applies a parallel tempering algorithm to study the first-order deconfinement transition in quenched QCD, achieving high-precision measurements of transition parameters by reducing auto-correlation issues.

Contribution

It demonstrates the effectiveness of parallel tempering in reducing auto-correlation times in lattice QCD simulations of the deconfinement transition.

Findings

Confirmed the first-order nature of the transition in the continuum limit.

Achieved per-mill precision in calculating the transition temperature.

Provided controlled continuum and infinite volume extrapolations.

Abstract

QCD with infinite heavy quark masses exhibits a first-order thermal transition which is driven by the spontaneous breaking of the global $\mathcal{Z}_3$ center symmetry. We analyze the corresponding order parameter, namely the Polyakov loop and its moments, and show, with a rigorous finite size scaling, that in the continuum limit the transition is of first order. We show that the use of a parallel tempering algorithm can significantly reduce the large auto-correlation times which are mainly caused by the supercritical slowing down. As a result, we calculate the transition temperature $w_0 T_c$ with per-mill precision, and the latent heat, carrying out controlled continuum and infinite volume extrapolations.