  Fermionic theories with a vanishing chiral condensate (in the chiral limit)
have recently attracted considerable interest; in particular variants of
multi-flavour QCD are candidates for this behaviour. Here we consider the
2-flavour Schwinger model as a simple theory with this property. Based on
simulations with light dynamical overlap fermions, we test the hypothesis that
in such models the low lying Dirac eigenvalues could be decorrelated. That has
been observed in 4d Yang-Mills theories at high temperature, but it cannot be
confirmed for the 2-flavour Schwinger model. We also discuss subtleties in the
evaluation of the mass anomalous dimension and its IR extrapolation.
