Drop model of infinite cluster for 2D percolation

Abstract

Computer-generated pictures of the connected component ('infinite cluster') and numerical results for conductivity made the authors realise the necessity of a proper treatment of inhomogeneity on scales smaller than the coherence length in 2D. They have developed a self-similar drop model of an infinite cluster and used it to construct a renormalisation group procedure and so to calculate properties of the system near the percolation threshold. They have predicted the dependence of the conductivity sigma and concentration of backbone B(L) on system size L at the percolation threshold. They obtain sigma approximately L^-t nu /, t/ nu =1, b approximately L^-x, where x= beta _B/ nu , beta _B=0.3.