  In the framework of Euclidean QCD on a torus, we study the spectrum of the
Dirac operator through inverse moments of its eigenvalues, averaged over
topological sets of gluonic configurations. The large-volume dependence of
these sums is related to chiral order parameters. We sketch how these results
may be applied to lattice simulations in order to investigate the chiral phase
transitions occurring when N_f increases. In particular, we demonstrate how
Dirac inverse moments at different volumes could be compared to detect in a
clean way the phase transition triggered by the suppression of the quark
condensate and by the enhancement of the Zweig-rule violation in the vacuum
channel.
