Numerical studies of critical percolation in three dimensions

Presents results of high-statistics simulations of the spreading of 3D percolation close to the critical point. The main results are: (i) a more precise estimate of the spreading (resp. 'chemical distance') dimension; (ii) a novel heuristic scaling theory for percolation near surfaces; and (iii) more precise values for critical surface and edge exponents. In addition, the author verifies the very precise results of Ziff and Stell (1988) for the percolation thresholds, and studies in detail corrections to scaling. The latter is made possible by simulating bond and site percolation, in a number of different geometries. In addition, in most cases one could measure more than one observable during each simulation, which provided quite severe internal consistency constraints. In some cases, the author found quite important deviations from scaling which are not easily described by a single power or logarithmic correction term.