A real-space renormalization group for site and bond percolation

Abstract

A real-space renormalization group is developed which renormalizes probabilities directly in the percolation problem. An exact transformation is given in one dimension, and a cluster approach is presented for other lattices. The results are in excellent agreement with series calculations for the critical percolation concentration p_c (both site and bond), and in good agreement for the correlation length exponent nu _p. Additionally, in one dimension, a field-like variable is included and the remaining exponents are calculated.