  For the calculation of the partition function $\mathcal{Z}$ of small,
isolated and interacting many body systems an improvement with respect to
previous formulations is presented. By including anharmonicities and employing
a variational approach quantum effects can be treated even at very low
temperatures. In order to test its accuracy the novel approach is applied to
the exactly solvable Lipkin-Meshkov-Glick model (LMGM). For thermodynamic
properties and level densities good agreement with the exact calculations is
found.
