Exact Phase Diagram of a model with Aggregation and Chipping

Abstract

We revisit 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 to a randomly chosen neighbour 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 ${\rho }_c(w)$. In this paper, we show analytically that in arbitrary spatial dimensions, ${\rho }_c(w)=\sqrt{w+1}-1$ exactly and hence, remarkably, independent of dimension. We also provide direct and indirect numerical evidence that strongly suggest that the mean field asymptotic answer for the single site mass distribution function and the associated critical exponents are super-universal, i.e., independent of dimension.

11 pages, RevTex, 3 figures

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• Exact Calculation of the Spatio-temporal Correlations in the Takayasu model and in the q-model of Force Fluctuations in Bead Packs
• Phase Transition in the Takayasu Model with Desorption

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