NUMERICAL-STUDIES OF CRITICAL PERCOLATION IN 3-DIMENSIONS

We present results of high-statistics simulations of the spreading Of 3D percolation close to the critical point. Our 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 adition, we verify the very precise results of Ziff and Stell for the percolation thresholds, and we study 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 we could measure more than one observable during each simulation, which provided us with quite severe internal consistency constraints. In some cases, we found quite important deviations from scaling which are not easily described by a single power or logarithmic correction term.