Percolation phenomena in higher dimensions: Approach to the mean-field limit

Percolation thresholds in two to six dimensions are studied by Monte Carlo methods in order to test Toulouse's recent conjecture that at six dimensions the Bethe lattice description of the threshold becomes exact. The results verify the existence of this critical dimensionality, but are only qualitatively in agreement with the predictions of expansions to 6-ε dimensions. © 1976 The American Physical Society.