About the Yukawa model on a lattice in the quenched approximation

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.