Phase Transition in the Takayasu Model with Desorption

Details Phase Transition in the Takayasu Model with Desorption Phase Transition in the Takayasu Model with Desorption

2000-01-19

arxiv.org/abs/cond-mat/0001277v1

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevE.61.6337

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 $pp_c(q)$, $P(m)\sim \exp(-m/m^*)$ for large $m$. The model is studied analytically within a mean field theory and numerically in one dimension.

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