The order of the chiral phase transition in massless many-flavour lattice QCD

TL;DR

This study investigates how the order of the chiral phase transition in massless many-flavour lattice QCD depends on the number of light quark flavours, revealing lattice artifacts and a tricritical line connected to the continuum.

Contribution

It maps out the chiral critical surface in lattice QCD, identifying tricritical points and their relation to the continuum limit across different quark flavours.

Findings

First-order transition region is a lattice artifact.

Critical temperature decreases with increasing number of flavours.

A tricritical line connects lattice artifacts to the continuum limit.

Abstract

The nature of the QCD phase transition in the chiral limit presents a challenging problem for lattice QCD. However, its study provides constraints on the phase diagram at the physical point. In this work, we investigate how the order of the chiral phase transition depends on the number of light quark flavours. To approach the lattice chiral limit, we map out and extrapolate the chiral critical surface that separates the first-order region from the crossover region in an extended parameter space, which includes the gauge coupling, the number of quark flavours, their masses, and the lattice spacing. Lattice simulations with standard staggered quarks reveal that for each $N_f < 8$, there exists a tricritical lattice spacing $a^\text{tric}(N_f)$, at which the chiral transition changes from first order ($a>a^\text{tric}$) to second order ($a<a^\text{tric}$). Thus, the first-order region is merely a lattice artifact and not connected to the continuum. By determining the associated temperatures $T(N_f^\text{tric},a ^\text{tric})$ at these tricritical points, we confirm the expected decrease in the critical temperature as the number of flavours increases. The obtained temperatures define a tricritical line which is connected to the continuum and terminates at a physical $ N_f^\text{tric}(a=0) $. Our data is compatible with a vanishing temperature at that point, $T(N_f^\text{tric}(a=0))=0 $.