In order to calculate expectation values such as the mean energy \langle E \rangle or magnetization \langle {\cal M} \rangle in statistical physics at a given temperature, we need a probability distribution \begin{equation*} P_i(\beta) = \frac{e^{-\beta E_i}}{Z} \end{equation*} with \beta=1/kT being the inverse temperature, k the Boltzmann constant, E_i is the energy of a state i while Z is the partition function for the canonical ensemble defined as \begin{equation*} Z=\sum_{i=1}^{M}e^{-\beta E_i}, \end{equation*} where the sum extends over all microstates M . P_i expresses the probability of finding the system in a given configuration i .