The largeNbehaviour of the Lipkin model and exceptional points

The ubiquitous Lipkin model is investigated for an interaction parameter beyond the traditional critical point. It is argued that a phase transition occurs higher up in the spectrum for such larger interaction, where, using appropriate scaling of the energies, the position of the phase transition becomes independent of the particle number. The phase transition is related to near singularities in the complex interaction plane, the exceptional points. Consideration of finite temperature yields the well-known physical features associated with phase transitions.