  The Schwinger model with $N_f \geq 2$ flavors is a simple example for a
fermionic model with zero chiral condensate Sigma (in the chiral limit). We
consider numerical data for two light flavors, based on simulations with
dynamical chiral lattice fermions. We test properties and predictions that were
put forward in the recent literature for models with Sigma = 0, which include
IR conformal theories. In particular we probe the decorrelation of low lying
Dirac eigenvalues, and we discuss the mass anomalous dimension and its IR
extrapolation. Here we encounter subtleties, which may urge caution with
analogous efforts in other models, such as multi-flavor QCD.
