QCD at zero baryon density

TL;DR

This paper compares grand canonical and canonical partition functions in QCD at zero baryon density, showing their equivalence in the thermodynamic limit and analyzing implications for the deconfinement transition.

Contribution

It demonstrates the formal and numerical equivalence of grand canonical and canonical ensembles in QCD at zero baryon density, especially regarding phase transition properties.

Findings

Differences between ensembles vanish with increasing lattice size.

Free energy density is identical in both ensembles in the thermodynamic limit.

Numerical simulations confirm theoretical predictions.

Abstract

While the grand canonical partition function Z_{GC}(mu) with chemical potential mu explicitly breaks the Z_3 symmetry with the Dirac determinant, the canonical partition function at fixed baryon number Z_C(B) is manifestly Z_3-symmetric. We compare Z_{GC}(mu=0) and Z_C(B=0) formally and by numerical simulations, in particular with respect to properties of the deconfinement transition. Differences between the two ensembles, for physical observables characterising the phase transition, vanish with increasing lattice size. We show numerically that the free energy density is the same for both ensembles in the thermodynamic limit.