Phase transition in the takayasu model with desorption

Abstract

We study a lattice model where particles carrying different masses diffuse and 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)∼m^-τ 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)∼m^-τ for large m as in the Takayasu case. For p=p_c(q), we find P(m)∼m^-τ_c where τ_c is a new exponent, while for p>p_c(q), P(m)∼exp(-m/m^∗) for large m. The model is studied analytically within a mean-field theory and numerically in one dimension.