Renormalisation-group results for bond and site percolation in two and three dimensions

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Abstract
Critical exponents and probabilities are calculated for bond and site percolation on the d=2 square lattice and the d=3 BCC lattice. The calculation exploits the relationship between the percolation problem and the s-state Potts model in the limit s to 1. The s-state Potts model is analysed using Kadanoff's variational renormalisation transformation. Results for the critical exponents and critical couplings of the s-state Potts model in the interval 0<or=s<or=1 are also presented.