Stability of lattice QCD simulations and the thermodynamic limit

We study the spectral gap of the Wilson-Dirac operator in two-flavour lattice QCD as a function of the lattice spacing a, the space-time volume V and the current-quark mass m. It turns out that the median of the probability distribution of the gap scales proportionally to m and that its width is practically equal to a/V1/2. In particular, numerical simulations are safe from accidental zero modes in the large-volume regime of QCD.