Precision study of the continuum SU(3) Yang-Mills theory: how to use parallel tempering to improve on supercritical slowing down for first order phase transitions

TL;DR

This study uses large-scale simulations and an improved parallel tempering algorithm to precisely characterize the first order phase transition in quenched QCD, overcoming critical slowing down.

Contribution

It introduces a generalized parallel tempering method that effectively mitigates supercritical slowing down in first order phase transitions in lattice QCD simulations.

Findings

First precise measurement of transition temperature $w_0T_c$=0.25384(23).

Accurate calculation of latent heat $ ext{Δ}E/T_c^4$=1.025(21)(27).

Demonstrated efficiency of parallel tempering in overcoming critical slowing down.

Abstract

We perform large scale simulations to characterize the transition in quenched QCD. It is shown by a rigorous finite size scaling that the transition is of first order. After this qualitative feature quantitative results are obtained with unprecedented precision: we calculate the transition temperature $w_0T_c$=0.25384(23), -- which is the first per-mill accurate result in QCD thermodynamics -- and the latent heat $\Delta E/T_c^4$=1.025(21)(27) in both cases carrying out controlled continuum and infinite volume extrapolations. As it is well known the cost of lattice simulations explodes in the vicinity of phase transitions, a phenomenon called critical slowing down for second order phase transitions and supercritical slowing down for first order phase transitions. We show that a generalization of the parallel tempering algorithm of Marinari and Parisi [Europhys. Lett. 19, 451 (1992)] originally for spin systems can efficiently overcome these difficulties even if the transition is of first order, like in the case of QCD without quarks, or with very heavy quarks. We also report on our investigations on the autocorrelation times and other details.