Spreading of percolation in three and four dimensions

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.