Large-Scale Simulations of Diffusion-Limited n-Species Annihilation

We present results from computer simulations for diffusion-limited $n$-species annihilation, $A_i+A_j\to 0$ $(i,j=1,2,\mathrm{.}\mathrm{.}\mathrm{.},n;i\mathrm{\ne }j)$, on the line, for lattices of up to $2^{28}$ sites, and where the process proceeds to completion (no further reactions possible), involving up to ${10}^{15}$ time steps. These enormous simulations are made possible by the renormalized reaction-cell method (RRC). Our results suggest that the concentration decay exponent for $n$ species is $\text{a}(n)=(n-1)\mathrm{/}2n$ instead of $(2n-3)\mathrm{/}(4n-4)$, as previously believed, and are in agreement with recent theoretical arguments \cite{tauber}. We also propose a scaling relation for $\mathrm{\Delta }$, the correction-to-scaling exponent for the concentration decay; $c(t)\sim t^{-\a}(A+Bt^{-\Delta})$.