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 pc (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.