Phase transition in the Takayasu model with desorption

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 w here the steady-state single site mass distribution has a power-law tail P( m)similar to m(-tau) for large mass. We show that varying the desorption ra te p induces a nonequilibrium phase transition in all dimensions. For fixed q, there is a critical p,(q) such that if p < p(c)(q), the steady-state ma ss distribution, P(m)similar to m(-tau) for large rn as in the Takayasu cas e. For p = P-c(q), we find P(m)similar to m(-tau c) where tau(c) is a new e xponent, while for p > p(c)(q), P(m)similar to exp(-m/m*) for large m. The model is studied analytically within a mean-held theory and numerically in one dimension.