Aggregate formation in a system of coagulating and fragmenting particles with mass-dependent diffusion rates

The effect of introducing a mass-dependent diffusion rate $\sim m^{-\alpha }$ in a model of coagulation with single-particle breakup is studied both analytically and numerically. The model with $\alpha =0\mathrm{}$ is known to undergo a nonequilibrium phase transition as the mass density in the system is varied from a phase with an exponential distribution of mass to a phase with a power-law distribution of masses in addition to a single infinite aggregate. This transition is shown to be curbed, at finite densities, for all $\alpha >0\mathrm{}$ in any dimension. However, a signature of this transition is seen in finite systems in the form of a large aggregate and the finite-size scaling implications of this are characterized. The exponents characterizing the steady-state probability that a randomly chosen site has mass m are calculated using scaling arguments. The full probability distribution is obtained within a mean-field approximation and found to compare well with the results from numerical simulations in one dimension.