Nonlinear conductivity of a disordered medium at the percolation threshold
Satanin A. M. , Khor'kov S. V., Ugol'nikov A. Yu.
It is shown that the effective nonlinear conductivity ae and the electric-field correlation function (e4) of a metal-insulator mixture at the percolation threshold grow as ae~h~"*, (e4)~h~e* for h<\, where Η — σ2Ι<Τ\ is the ratio of linear conductivities. Dykhne's relations are used to derive important inequalities for the nonlinear conductivity and the critical exponents. The quantities ae and {e4) as functions of h were found by numerical modeling on a 100X 100 grid and the critical exponents were calculated: и4= e4= 1.33±0.05. © 1995 American Institute of Physics.
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![](/ps/1215/article_18371_800_head.png "It is shown that the effective nonlinear conductivity <i>a<sub>e</sub> </i>and the electric-field correlation function (e<sup>4</sup>) of a metal-insulator mixture at the percolation threshold grow as <i>a<sub>e</sub>~h~"*, (e<sup>4</sup>)~h~<sup>e</sup>* </i>for <i>h<\, </i>where <i>Η — σ<sub>2</sub>Ι</i><b><i><Τ\ </i></b>is the ratio of linear conductivities. Dykhne's relations are used to derive important inequalities for the nonlinear conductivity and the critical exponents. The quantities <i>a<sub>e</sub> </i>and {e<sup>4</sup>) as functions of <i>h </i>were found by numerical modeling on a 100X 100 grid and the critical exponents were calculated: и<sub>4</sub>= e<sub>4</sub>= 1.33±0.05. © <i>1995 American Institute of Physics.</i>")