Exact phase diagram of a model with aggregation and chipping
Abstract
We reexamine a simple lattice model of aggregation in which masses diffuse and coalesce upon contact with rate 1 and every nonzero mass chips off a single unit of mass and adds it to a randomly chosen neighbor with rate w. The dynamics conserves the average mass density ρ and in the stationary state the system undergoes a nonequilibrium phase transition in the (ρw) plane across a critical line ρ_{c}(w). In this paper, we show analytically that in arbitrary spatial dimensions ρ_{c}(w)=w+11 exactly and hence, remarkably, is independent of dimension. We also provide direct and indirect numerical evidence that strongly suggests that the mean field asymptotic results for the single site mass distribution function and the associated critical exponents are superuniversal, i.e., independent of dimension.
 Publication:

Physical Review E
 Pub Date:
 March 2001
 DOI:
 10.1103/PhysRevE.63.036114
 arXiv:
 arXiv:condmat/0009110
 Bibcode:
 2001PhRvE..63c6114R
 Keywords:

 64.60.i;
 05.70.Ln;
 General studies of phase transitions;
 Nonequilibrium and irreversible thermodynamics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 11 pages, RevTex, 3 figures