QCD at zero baryon density

While the grand canonical partition function ZGC(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.