Peczak [*et al.*]{} [@r18]. We analyzed this run to locate a first estimate for the temperatures of the maxima of the specific heat and the susceptibility for each $L$, and used those two temperatures for our other two simulations. This choice has the advantage that both locations of the maxima scale approximately like $L^{-1/\nu}$ which is also the region after which the energy distribution $P_\beta(E)$ has decreased by roughly the same factor for all $L$. We can therefore expect to have always enough overlap to ensure a safe reweighting of our three histograms into the $\beta$-region of interest. A further advantage is that the two maxima approach $T_c$ from different sides.

For each configuration we recorded the energy histogram $P_\beta(E)$, using 90000 bins to discretize the continuous energy range $0 \le E \le 3V$. We have checked that this binning is fine enough to ensure negligibly small discretization errors. In addition we recorded the microcanonical averages of $\langle\!\langle m \rangle\!\rangle(E)$, $\langle\!\langle m^2 \rangle\!\rangle(E)$, and $\langle\!\langle m^4 \rangle\!\rangle(E)$. These histograms provided us with all necessary information to calculate all thermodynamic quantities of interest. Every 10000 measurement steps we recorded a copy of each histogram, so that we were able to compute 