  Random Matrix Theory (RMT) has elaborated successful predictions for Dirac
spectra in field theoretical models. However, a generic assumption by RMT has
been a non-vanishing chiral condensate $\Sigma$ in the chiral limit. Here we
consider the 2-flavour Schwinger model, where this assumption does not hold. We
simulated this model with dynamical overlap hypercube fermions, and entered
terra incognita by analysing this Dirac spectrum. The usual RMT prediction for
the unfolded level spacing distribution in a unitary ensemble is precisely
confirmed. The microscopic spectrum does not perform a Banks-Casher plateau.
Instead the obvious expectation is a density of the lowest eigenvalue
$\lambda_{1}$ which increases $\propto \lambda_{1}^{1/3}$. That would
correspond to a scale-invariant parameter $\propto \lambda V^{3/4}$, which is,
however, incompatible with our data. Instead we observe to high precision a
scale-invariant parameter $z \propto \lambda V^{5/8}$. This surprising result
implies a microscopic spectral density $\propto \lambda_1^{3/5}$, which still
remains to be understood in the light of RMT.
