Conserved mass aggregation model with mass-dependent fragmentation

We study a conserved mass aggregation model with mass-dependent fragmentation in one dimension. In the model, the whole mass $m$ of a site isotropically diffuse with unit rate. With rate $ω$, a mass $m^λ$ is fragmented from the site and moves to a randomly selected nearest neighbor site. Since the fragmented mass is smaller than the whole mass $m$ of a site for $λ< 1$, the on-site attractive interaction exists for the case. For $λ= 0$, the model is known to undergo the condensation phase transitions from a fluid phase into a condensed phase as the density of total masses ($ρ$) increases beyond a critical density $ρ_c$. For $0< λ<1$, we numerically confirm for several values of $ω$ that $ρ_c$ diverges with the system size $L$. Hence in thermodynamic limit, the condensed phase disappears and no transitions take place in one dimension. We also explain that there are no transitions in any dimensions.

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