Exceptional points of a Hamiltonian and phase transitions in finite systems

For a model Hamiltonian which describesN interacting Fermions and which is typical for systems that undergo phase transitions it is shown that for finiteN the transitional point is associated with exceptional points of the Hamiltonian. In the limit of largeN these singularities move down to the real axis. The nature of the limit turns out to be quite different depending on whether it is taken for interaction strengths smaller or larger than the critical value.