Finite Temperature Many-Body Theory with the Lipkin Model

We have compared exact numerical results for the Lipkin model at finite temperature with Hartree-Fock theory and with the results of including in addition the ring diagrams. In the simplest version of the Lipkin model the Hartree-Fock approach shows a ``phase transition" which is absent in the exact results. For more realistic cases, Hartree-Fock provides a very good approximation and a modest improvement is obtained by adding the ring diagrams.