Phase Transition in the Takayasu Model with Desorption

Abstract

We study a lattice model where particles carrying different masses diffuse, coalesce upon contact, and also unit masses adsorb to a site with rate $q$ or desorb from a site with nonzero mass with rate $p$. In the limit $p=0$ (without desorption), our model reduces to the well studied Takayasu model where the steady-state single site mass distribution has a power law tail $P(m)\sim m^{-\tau }$ for large mass. We show that varying the desorption rate $p$ induces a nonequilibrium phase transition in all dimensions. For fixed $q$, there is a critical $p_c(q)$ such that if $p<p_c(q)$, the steady state mass distribution, $P(m)\sim m^{-\tau }$ for large $m$ as in the Takayasu case. For $p=p_c(q)$, we find $P(m)\sim m^{-{\tau }_c}$ where ${\tau }_c$ is a new exponent, while for $p>p_c(q)$, $P(m)\sim \exp (-m/m^{\ast })$ for large $m$. The model is studied analytically within a mean field theory and numerically in one dimension.

RevTex, 11 pages including 5 figures, submitted to Phys. Rev. E

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