QCD at zero baryon density

While the grand canonical partition function ZGC(μ) with chemical potential μ explicitly breaks the Z3 symmetry with the Dirac determinant, the canonical partition function at fixed baryon number Zc(B) is manifestly Z3-symmetric. We compare ZGC (μ = 0) and ZC (B = 0) formally and by numerical simulations, in particular with respect to properties of the deconfinement transition. The small differences between the two ensembles vanish with increasing lattice size. We show numerically that the free energy density is the same for both ensembles in the thermodynamic limit. As a function of the chemical potential, the pressure is close to its Stefan-Boltzmann limit for T ∼ 1.1Tc already. (author)