The starry sky model of the percolation phase transition II. The conductivity backbone created by the Hall coefficient

A ‘special nodes and blobs’ model of percolation phase transition, obtained from the distribution function of a kinetic coefficient, such as conductivity and the Hall and Seebeck coefficients, is introduced. Principally, the difference from the previous models is that the ‘special’ nodes are responsible for almost all values of the kinetic coefficient (for example the resistivity of system). The ‘special’ nodes, which can appear or disappear like stars in the sky, enable one to construct, below the threshold, a two-component conductivity backbone, in terms of which a new order parameter for metal-superconductor transition can be obtained. The fractal dimension of the conductivity backbone for both sides of the threshold is dBƒ = d − g/v = 2.25 where G = 0.6 is a critical exponent of the Hall coefficient in d = 3 dimensions. The customary fractal dimension of the backbone in percolation dBƒ = 1.8 is interpreted as fractal dimension of connectivity backbone.