them by anisotropic particles with a finite aspect ratio of the order of $k^*= m/L$.

Although Model II looks a little bit more realistic, Model I has previously been widely used.​ This is the reason why all our computations were performed within the frameworks of both models. Figure \[fig:compare\] presents examples of comparison of the electrical conductivity, $\sigma$, versus the filling fraction, $p$, for both models. We have found that differences in the results are of the same order as the statistical errors. Therefore, in this article we have presented all the results only for Model II. Throughout the text, the error bars in the figures correspond to the standard deviations of the means. When not shown explicitly, they are of the order of the marker size.

![Comparison of the results obtained within the frameworks of Models I and II. Electrical conductivity, $\sigma$, versus the filling fraction, $p$, for $m=2048$ and $s=0.8$. Here, the filled and open symbols correspond to the longitudinal and transversal directions, respectively. The lines are provided simply as visual guides. Solid lines correspond to Model I, dashed lines correspond to Model II.\[fig:compare\]](conductvspcompare "fig:"){width="0.9\linewidth"}\

The filling fraction (optical absorbance of the 2D film), $p$, defined as the 