  We study the Yukawa model on a 4-dimensional Euclidean lattice in the
quenched approximation. A particular attention is given to the singularities of
the Dirac operator in the phase diagram. A careful analysis of a particular
limiting case shows that size effects can be huge, questioning the quenched
approximation. This is confirmed by a Monte-Carlo simulation in this limit case
and without the quenched approximation. We include also some results concerning
the symmetries of this model.
