  Strong repulsive interactions between electrons can lead to a Mott
metal-insulator transition. The Dynamical Mean-Field Theory (DMFT) explains the
critical end-point and hysteresis region with single-particle concepts such as
the spectral function and the quasiparticle weight. In this work, we reconsider
the critical end point of the metal-insulator transition on the two-particle
level. We show that the relevant eigenvalue and eigenvector of the non-local
Bethe-Salpeter kernel provide a unified picture of the hysteresis region and of
the critical end point of the Mott transition. In particular, they
simultaneously explain the thermodynamics of the hysteresis region and the
iterative stability of the DMFT equations. This analysis paves the way for a
deeper understanding of phase transitions in correlated materials.
