Differences Between Classical and Superconductive Percolation Fractals

Abstract

The average mass of the backbone has fractal dimensionalities [Formula: see text] for superconductive percolation and theat of classical percolation [Formula: see text] in dimensions d = 3, 4, 5 and 6 respectively. A new fractal dimension of "dead ends" [Formula: see text] refers to the difference between two percolations, because if most of the mass of the backbone belong to the dead ends, the superconductive behavior becomes impossible. The definition of the minimum path (or the chemical distance) and its fractal dimensionality does not exist in the superconductive percolation. Instead of the "red" bonds in classical percolotion, one has the real physical phenomena — the "special" nodes, which can be found in the experimental investigations. The order of ramification R for superconductive fractals is equal to the critical exponent of the number of the "special" nodes N(p) ∝ (p - pc)dν, (R = dν). The fractal dimension of order of ramification equals to zero.