Non-equilibrium phase transition and cluster size distribution in aggregation and weighted-fragmentation processes

Abstract

Through numerical simulations, we investigate the influence of an index ϕ on the cluster size distribution in aggregation and weighted-fragmentation processes where a decomposed cluster of size a is selected with a power-law weight W(a)∝aϕ. We reveal the existence of a non-equilibrium phase transition from an exponentially decayed phase to a partially condensed phase and calculate the threshold ϕc for this phase transition. For ϕ>ϕc, cluster size distribution asymptotically obeys exponential decay, which results in the largest cluster sized on the order of lnN, where N is a total cluster number. Exponential decay rates are computed as a function of ϕ. It is notable that the curvature of the distribution changes its sign at ϕ=1. For ϕ<ϕc, a partially condensed phase takes place and one big cluster sized on the order of a total monomer number M emerges and coexists with small clusters.