Beyond the Thouless energy

The distribution and the correlations of the small eigenvalues of the Dirac operator are described by random matrix theory (RMT) up to the Thouless en ergy E-c proportional to 1/root V, where V is the physical volume. For some what larger energies, the same quantities can be described by chiral pertur bation theory (chPT). For most quantities there is an intermediate energy r egime, roughly 1/V < E < 1/root V, where the results of RMT and chPT agree with each other. We test these predictions by constructing the connected an d disconnected scalar susceptibilities from Dirac spectra obtained in quenc hed SU(2) and SU(3) simulations with staggered fermions for a variety of la ttice sizes and coupling constants. In deriving the predictions of chPT, it is important to take into account only those symmetries which are exactly realized on the lattice.