Segregation in diffusion-limited multispecies pair annihilation

The kinetics of the q species pair annihilation reaction (A(i) + A(j) --> circle divide for 1 less than or equal to i < j less than or equal to q) in d dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time regime the total particle density decays as rho(t) similar to t(-alpha). For d = 1 the system segregates into single-species domains, yielding a different value of alpha for each q; for a simplified version of the model in one dimension we derive alpha (q) = (q - 1) / (2q). Within mean-field theory, applicable in d greater than or equal to 2, segregation occurs only for q < 1 + (4/d). The only physical realization of this scenario is the two-species process (q = 2) in d = 2 and d = 3, governed by an extra local conservation law. For d greater than or equal to 2 and q greater than or equal to 1 + (4/d) the system remains disordered and its density is shown to decay universally with the mean-field power law (alpha = 1) that also characterizes the single-species annihilation process A + A --> circle divide.