Exact phase diagram of a model with aggregation and chipping

We reexamine a simple lattice model of aggregation in which masses diffuse and coalesce upon contact with rate $1$ and every nonzero mass chips off a single unit of mass and adds it to a randomly chosen neighbor with rate w. The dynamics conserves the average mass density $\rho$ and in the stationary state the system undergoes a nonequilibrium phase transition in the $(\rho -w)$ plane across a critical line ${\rho }_c\mathrm{}\left(w\right).$ In this paper, we show analytically that in arbitrary spatial dimensions ${\rho }_c\mathrm{}\left(w\right)=\sqrt{w+1\mathrm{}}-1$ exactly and hence, remarkably, is independent of dimension. We also provide direct and indirect numerical evidence that strongly suggests that the mean field asymptotic results for the single site mass distribution function and the associated critical exponents are superuniversal, i.e., independent of dimension.