DIFFUSION-CONTROLLED BINARY REACTIONS IN LOW DIMENSIONS - REFINED SIMULATIONS

Refined Monte Carlo simulations have been performed on the diffusion-controlled A + B --> 0 and A + A --> 0 reaction on two- and three-dimensional critical percolation clusters and in one dimension. For comparison, we also tested the single random walker S(N) (number of distinct sites visited in N steps). Effects of excluded volume, time counting, random number generators, averaging procedures, and boundary conditions have been tested and found to be within our simulation uncertainties. However, finite-size and finite-time effects are important, as well as the initial particle density and the number of runs. All the A + A and S(N) data agree with the well-known scaling predictions, i.e., the time exponent is d(s)/2, where d(s) is the spectral (fracton) dimension. The same is true for A + B reactions in one dimension (the exponent being 1/4). Finally, for the A + B reactions on two- and three-dimensional critical percolation clusters, our refined data are consistent with the classical Kang and Redner [Phys. Rev. Lett. 52, 944 (1984)] scaling result as well as the bounds (given in more recent work) involving other fractal dimensions.