Annihilation reactions in two-dimensional percolation clusters: Effects of short-range interactions

We report Monte Carlo simulations of annihilation reaction A+A→0 in two-dimensional percolation clusters. In the model, the particles diffuse coupled by nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions. The following cases have been studied: (i) repulsive NN interaction, (ii) repulsive NN and NNN interactions, and (iii) repulsive NN and attractive NNN interactions. In the intermediate-time regime, for cases (i) and (ii), we found that the density of particles ρ approximately decays as ρ∼t^-γ(2/3<γ<1), where γ depends on specific values of interactions but is independent of the initial density ρ(t=0). For case (iii) there is no power-law decay. For the short- and intermediate-time regimes, a scaling ansatz for cases (i) and (ii) is found.