The scalar and vector percolation

Classical (scalar) percolation is described the behavior of a classical particle with resistivity along the path, that is based on a suggestion that the physics of disordered systems near the threshold is dominated by singly connected `redʹ bonds. In term of the resistor network, these bonds carry the full current which goes through the circuit. The problem is that percolation is a vector process. Only the universal model that covers scalar and vector cases simultaneously can give a real picture of the percolation phase transition. Based on the Hall coefficient, Youngʹs modulus and the Joule heat distribution functions, superconductive (rigid) percolation exact shows that the physics of disordered systems near the threshold is dominated by the poles, whose behavior are very different from singly connected `redʹ bonds. The current does not go through the `redʹ bonds but avoids them as soon as possible by choosing the easier path to flow. As a result, we have found unexpected paradoxical situation in the percolation transition: the superconductive behavior below and above the threshold. The average mass of the backbone is proportional to the reciprocal Hall coefficient Re(p)∝(p−pc)g, g=0.6, and describes by the fractal dimensionalities dfB=d−g/ν=2.32;2.85;3.47;3.8 for the superconductive percolation, whereas that of the classical percolation equals dfB=1.82;1.901.93;2 in dimensions d=3, 4, 5 and 6, respectively.