Statistical and finite size scaling behavior of the red bonds near the percolation threshold

By taking advantage of a new algorithm providing for the first time the current intensity in each link of a square resistor network, we study near the percolation threshold the statistical and scaling properties of red bonds (links of the backbone carrying the total current injected to the system). Two branches appear in the red bonds distribution, one is power law decreasing for small numbers of these bonds and the other one is log-normal. This shape of the distribution leads to very large fluctuations of this number with a power-low scaling exponent shifted to lower values compared to that known for infinite systems. The geometric average seems to behave statistically better and provides scaling exponents faster converging to the thermodynamic limit exponent 1/ν (ν being the correlation length exponent).