what we find on our $L=20$ and $L=32$ lattices with the latter. This is done in Table \[table\_length\]. There we show the longest and shortest cluster lengths for the largest, second largest and third largest cluster respectively over the ensemble. The ensemble sizes are not exactly the same, but it is nonetheless clear that there is a real gulf between the largest and second largest clusters on the $L=32$ lattice while there is significant overlap in the $L=16$ case. The $L=20$ lattice is a marginal case. We conclude from this that the apparent loss of a well separated largest cluster as seen in [@hart98] at $\beta=2.5$ was in fact a finite volume effect, and that our scaling analysis has proved reliable in predicting what volume one needs to use in order to regain the simple picture.

In Figure \[fig\_curr\_dens\] we show how the length of the largest cluster varies with the lattice volume when both are expressed in physical units (set by $\sqrt{K}$). To be specific, we have divided $l_{\max}\sqrt{K}$ by $(L\sqrt{K})^4$ and plotted the resulting numbers against $L\sqrt{K}$ for both our new and our old calculations. The fact that at fixed $\beta$ the values fall on a horizontal line 