ABSTRACTThe diffusion-limited annihilation reactions A+A→products and A+B→products havebeen subject to theoretical, numerical, and experimental study over the past decade. “Anomalous” behaviors have been reported for both reactions, but with different upper critical dimensions (d=2 and d=4 respectively). The critical dimensions and the scaling of the exponents for the generalized reaction nA+mB→products depends on n and m. We present Monte Carlo simulations for two different types of third-order reactions, A+A+A→0 and A+2B→0, on both one and two dimensional lattices. Our numerical results show that for the two-dimensional case the behavior of the reaction follows mean-field theory while in one dimension the result is“anomalous”. Our numerical results are in good agreement with theory based on microscopic arguments and scaling analysis.
