I'm writing with respect to this paper: Khatun, Dutta, and Tarafdar - "Islands in Sea" and "Lakes in Mainland" phases and related transitions simulated on a square lattice

Here's a link to the PDF version.

The following graph shows the number of clusters (black and white respectively) per unit area for any $p\in [0,1]$, where $p$ is the probability of a square being black, for different system sizes ($L=8/16/32/64/128/256$ units). (Please read the abstract I linked for a brief explanation of the type of system we're dealing with.)

Is there any method to exactly calculate the $p$, for which the maxima of the curves (of black clusters, and white clusters) occur when $L\to\infty$ ?

Yes, I know that I can do numerical testing and then use extrapolation, but I don't want to do that as extrapolation often predicts values with large amount of error.

thinkthe limiting graph would have a similar nature with a maxima somewhere before $p=0.5$ for the black cluster graph and somewhere after $p=0.5$ for the white cluster graph. $\endgroup$ – user119567 Mar 11 '18 at 21:08