Reaction symmetry of irreversible reaction nA+mB-->0

We investigate the kinetics of irreversible reaction nA+mB-->0. When nA particles and mB particles encounter on the same site, the reaction takes place. We classify the reaction into two classes, the symmetric and the asymmetric reactions. The symmetric reaction means both nA+mB-->0 and mA+nB-->0, while the asymmetric reaction means only nA+mB-->0 for a given (n,m) pair. The kinetics of the reaction follows the fluctuation-dominated kinetics of A+B-->0 for Nor=Nc, the kinetics follows a mean-field rate equation. For the asymmetric reaction, it was shown that Nc is 5. We numerically show that the reaction symmetry changes Nc in one dimension. We investigate the asymptotic scaling behaviors of density and various lengths characterizing the spatial organization of particles such as domain length and interparticle distance. Lengths exhibit much clear crossover to the mean-field region at the expected Nc of each reaction. From the scaling behavior of density and lengths, we show Nc=4 for the symmetric reaction in one dimension. Therefore the symmetry in the reaction changes the upper critical dimension, which implies that the kinetics cannot be described by a single theory.