About the Yukawa model on a lattice in the quenched approximation

TL;DR

This paper investigates the Yukawa model on a 4D lattice, analyzing the effects of the quenched approximation and singularities, and compares quenched and unquenched results through simulations.

Contribution

It provides a detailed analysis of the Yukawa model's phase diagram, highlighting the limitations of the quenched approximation and exploring symmetry properties.

Findings

Size effects can be significant, challenging the validity of the quenched approximation.

Monte-Carlo simulations confirm large size effects in the quenched limit.

Symmetry properties of the model are also examined.

Abstract

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.