An infinitesimal renormalisation-group transformation for the site percolation problem
- 30 June 1980
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 13 (18) , 3387-3401
- https://doi.org/10.1088/0022-3719/13/18/007
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.Keywords
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