Spreading of percolation in three and four dimensions
- 21 June 1986
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 19 (9) , 1681-1689
- https://doi.org/10.1088/0305-4470/19/9/038
Abstract
The authors present Monte Carlo simulations of the spreading of bond percolation on three- and four-dimensional simple (hyper-)cubic lattices. The algorithm is the same as that applied previously in two dimensions, with the spreading proceeding from a hyperplane. They find the spreading dimension to be d=1.82+or-0.02 (three-dimensional) and d=1.88+or-0.03 (four-dimensional). Also they obtain values of the percolation probability and of the static exponents with errors at least comparable to the best values from the literature.Keywords
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