Abstract

The site percolation problem is studied by an infinitesimal (i.e. the scaling factor b to 1) renormalisation transformation. The correlation length exponent v, the 'magnetic' scaling power yh and the three independent conductivity exponents t, s and v are calculated. It is shown that only the shortest one-dimensional percolation paths are important in the derivation of renormalised probabilities and conductances. This explains why two different transformations-one for the site percolation problem and the other for the bond percolation problem-become equivalent in the b to 1 limit.

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