Simulation of percolation on massively-parallel computers

A novel approach to parallelize the well-known Hoshen-Kopelman algorithm has been chosen, suitable for simulating huge lattices in high dimensions on massively-parallel computers with distributed memory and message passing. This method consists of domain decomposition of the simulated lattice into strips perpendicular to the hyperplane of investigation that is used in the Hoshen-Kopelman algorithm. Systems of world record sizes, up to L = 4 000 256 in two dimensions, L = 20 224 in three, and L = 1036 in four, gave precise estimates for the Fisher exponent r, the corrections to scaling Delta (1), and for the critical number density n(c).