On the Thermodynamic Limit of the Lipkin Model

The thermodynamic limit of the Lipkin model is investigated. While the limit turns out to be rather elusive, the analysis gives strong indications that the limit yields two analytically dissociated operators, one for the normal and one for the deformed phase. While the Lipkin Hamiltonian is hermitian and has a second order phase transition in finite dimensions (finite particle number), both properties seem to be destroyed in the thermodynamic limit.