  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.
