Analytic solution of the block-cluster theory of site and bond percolation in arbitrary dimension
Garnet N. Ord, B. Payandeh, M. Robert
The percolation transition in arbitrary dimension is studied in real space by generalizing the block-cluster theory. For both site and bond percolation on a decorated hypercubic lattice, this theory yields analytic renormalization-group equations in any number of dimensions. For bond percolation, these analytic equations are most remarkably simple. Results are presented for the thermal exponent and compare very favorably with results obtained by other methods. This is the first successful renormalization-group theory in real space in which the dimension of space enters as a variable parameter.
Physical review. B, Condensed matter•Jan 1, 1988•5 citations