THE ANNIHILATING RANDOM-WALK AS A MODEL FOR DOMAIN GROWTH IN ONE-DIMENSION

We are presenting results of a Monte Carlo simulation of the one-dimensional annihilating random walk (ARW). If the system size is not very large with respect to the mean interparticle distance, time-dependent finite-size effects arise and additional correlations between particles are introduced. Monte Carlo results are analysed in terms of simple analytical approximations. Using the equivalence to the kinetic Ising model at zero temperature and zero initial magnetization, we investigate the dependence of the square of the magnetization on the interparticle distance distribution. Finally, neglecting correlations, an analytical approximation for the asymptotic interparticle distance distribution in an infinite system is derived.