The starry sky model of the percolation phase transition I. The ‘special’ nodes

The real physical phenomena of ‘special’ nodes in a percolation phase transition, obtained from the distribution functions of the Joule heat and the Hall and Seebeck coefficients are considered. The ‘special’ nodes N (p) (the ‘active’ nodes for the Hall and Seebeck coefficients and the ‘hot’ nodes for conductivity) have the same coordinate, but belong to different components below and above the threshold. The Hall (and the thermo) batteries, which are developed in the ‘active’ nodes, are responsible for the almost all effective Hall (or Seebeck) current, whereas the ‘hot’ nodes have taken almost all Joule heat. In the critical interval, ‘special’ nodes always exist for conductivity and may disappear or appear (like the stars in the sky) for Hall and Seebeck coefficients. In the latter case, the kinetic coefficients can be characterized by the new critical exponents, different from conductivity, and belong to a different universality class. It leads to the different models of ‘nodes and blobs’ for each kinetic coefficient. The fractal dimension of N (p) equals zero