Two-dimensional site-bond percolation as an example of self-averaging system

The Harris-Aharony for statical model criteria predicts, that if specific heat exponent $\alpha \ge 0$, then this model does not exhibit self-averaging. In two-dimensional percolation model the index $\alpha=-\frac{1}{2}$. It means, that in accordance with Harris-Aharony criteria, this model can exhibit self-averaging properties. We study numerically the relative variance $R_{M}$ and $R_{\chi}$ of the probability of site to belong the «infinite» (maximum) cluster $M$ and the mean finite cluster sizes $\chi$. It was shown, that two-dimensional site-bound percolation on the square lattice, where the bonds play role of impurity and sites play role of statistical ensemble, over which the averaging performed, exhibit self-averaging properties.