Nonuniversality and breakdown of scaling in two-species aggregation

A simple model of aggregation is presented which is built from two distinct monomeric species, A and B, with bonding allowed only between unlike species. This model exhibits novel and unexpected kinetic behavior which depends crucially on whether the mass of the aggregate is odd or even. The kinetics of the even clusters can be accounted for within the framework of the single-species reaction scheme A+A→A, while the odd clusters can be described by the two-species reaction A+B→inert. Consequently, the upper critical dimension, $d_c$, for the kinetics of the even clusters is two, while $d_c$=4 for the odd clusters. Numerical simulations of this A-B model reveal unusual kinetic behavior, including novel dimension dependence below the upper critical dimension, nonuniversality, and a breakdown of scaling for the cluster-mass distribution. The underlying parity dependence of the A-B model leads us to introduce a simpler one-component aggregation model in which the reaction rates depend explicitly on the parity of the reacting clusters. The corresponding rate equations are studied and exact expressions for the exponents describing the decay rate of the aggregates are obtained. It is found that the kinetics of clusters of even and odd mass are, in general, quite different, and that the corresponding exponents are also generally nonuniversal. Furthermore, in two special cases, the complete solution to the rate equations can be obtained, and it is thus demonstrated that a conventional scaling description for the cluster-mass distribution breaks down.