The chiral limit $~\kappa \simeq \kappa_c(\beta)~$ in lattice gauge theories with Wilson fermions and problems related to near--to--zero ('exceptional') eigenvalues of the fermionic matrix are studied. For this purpose we employ compact lattice QED in the confinement phase. A new estimator $~\mpr_{ \pi}~$ for the calculation of the pseudoscalar mass $~m_{ \pi}~$ is proposed which does not suffer from 'divergent' contributions at $\kappa \simeq \kappa_c(\beta)$. We conclude that the main contribution to the pion mass comes from larger modes, and 'exceptional' eigenvalues play { \it no} physical role. The behaviour of the subtracted chiral condensate $~\langle \psb \psi \rangle_{ subt}~$ near $~\kappa_c(\beta)~$ is determined. We observe a comparatively large value of $~\langle \psb \psi \rangle_{ subt} \cdot Z_P^{ -1}~$, which could be interpreted as a possible effect of the quenched approximation.
Categories: hep-lat