A Nucleation Process Drives the Percolation Transition

Abstract

The new "special" nodes — the nucleation nodes, which drive the percolation transition for kinetic coefficients are found by using the distribution functions of kinetic coefficients such as conductivity, the Hall and Seebeck coefficients for the resistor network. They belong to the component, opposite to the "special" nodes and create an infinite cluster below the threshold and destroy it above the threshold. We have divided the "backbone" of an infinite cluster into two parts: (1) the static part which is responsible for analytic background; and (2) the dynamic part or a "scaling region" which equals the volume of the "special" nodes and is responsible for the singular part of kinetic coefficients and probably also for thermodynamic functions.