In our case we have as the Monte Carlo sampling function the probability for finding the system in a state s given by \begin{equation*} P_s=\frac{e^{-(\beta E_s)}}{Z}, \end{equation*} with energy E_s , \beta=1/kT and Z is a normalization constant which defines the partition function in the canonical ensemble. As discussed above \begin{equation*} Z(\beta)=\sum_se^{-(\beta E_s)} \end{equation*} is difficult to compute since we need all states.