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

The Harris-Aharony criterion for a static model predicts that if a specific heat exponent α>0, then this model does not exhibit self-averaging. In the two-dimensional percolation model, the index α= ?1/2. This means that, in accordance with the Harris-Aharony criterion, the model can exhibit self-averaging properties. We study numerically the relative variances R _M and R _χ for the probability M of a site belonging to the “infinite” (maximum) cluster and for the mean finite-cluster size χ. It was shown that two-dimensional site-bond percolation on the square lattice, where the bonds play the role of the impurity and the sites play the role of the statistical ensemble over which the averaging is performed, exhibits self-averaging properties.