Position-space renormalization of the percolation conduction problem

Abstract

A renormalization method recently proposed by Stinchcombe and Watson (ibid., vol.9, p.3221 (1976)) for the percolation conduction problem is modified by the introduction of a scheme for construction of the renormalization transformation based on a periodization of the lattice. There results a family of transformations, in which the larger domains give rise to the transformations which are increasingly more accurate (but more difficult to implement). The three exponents s, t and v are estimated for several two-dimensional cases and one three-dimensional case.