Crossover exponents in percolating nonlinear normal conductor–insulator mixtures

The critical behavior of nonlinear properties is studied in d-dimensional percolating weakly nonlinear normal conductor (N)–insulator (I) composites near the percolation threshold, in which the concentration p of normal conductor (N) obeys weakly nonlinear current density (J)-electric field (E) characteristics J=σ1E+χ1EβE and concentration 1−p of insulator (I) has σ2=0. Above the percolation threshold pc of the normal conductor, the effective response of the composites can be represented by J =σe E +χe E β E , where represents spatial averages, σe and χe are the effective linear and nonlinear response of the system. The magnitudes of the crossover field Ec and current density Jc, defined as the electric field and the current density at which the effective linear and nonlinear response become comparable, are found to have the power-law dependence Ec (p−pc)M(β) and Jc (p−pc)N(β) as the percolation threshold is approached from above. Here M(β) and N(β) are critical exponents and depend on dimensionality d and nonlinearity β in general. By means of effective medium approximation, “Nodes-Links-Blobs” picture and the relation to resistance fluctuation, respectively, we investigate the influence of nonlinearity β and dimensionality d on these crossover exponents in detail. Interesting crossover behavior is found in the two-dimensional system.