CURRENT DISTRIBUTION AND MOMENTS OF THE LOGARITHM OF THE CURRENTS IN PERCOLATING RESISTOR NETWORKS

Abstract

We reconsider the current distribution in percolating resistor networks. By comparing the analytic solution of the current distribution for a hierarchical model with the numerical data from a Monte Carlo simulation and exact enumerations, we propose a function to discribe the behavior of the current distribution of percolating resistor networks. In addition, we study the finite-size-dependent behavior of the moments of the logarithm of the currents. The q-th moment, mu(q), of log-currents exhibits unifractal behavior with respect to In L as mu(q) approximately B(q)(lnL)q for all q. However, it is found that the amplitude B(q) behaves as lnB(q) approximately qlnq for q>0 and approximately q for q<0 in the thermodynamic limit.