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.