LETTER TO THE EDITOR Two-dimensional diffusion limited aggregation: a finite-size scaling approach

Abb.rr Finite-size scaling in the diffusion-limited aggregation model of Witten and Sander is studied in two dimensions via Monte-Carlo simulations on semi-infinite strips of width n = 2-20. Due to a crossover between self-avoiding walk-like growth for small n and dendritic growth for large n, wide strips (n = 8-20) are needed to deduce the Witten-Sander fractal dimension D-f from the finite-size scaling analysis. The irreversible aggregation of small particles to build randomly ramified clusters is of interest in a wide variety of problems ranging from the coagulation of smoke particles (Forrest and Witten 1979) to the growth of crystals from an undercooled melt or a supersaturated solution (Langer 1980). Since the diffusion of the particles towards the cluster surface is often the rate-limiting process, Witten and Sander (1981, 1983) considered a simple lattice model in which a seed particle is placed at the centre of a large hypersphere at t = 0, then a new particle is released at random on the sphere and performs a random walk on the lattice until it reaches a site adjacent to the seed where it stops, building a two-particle cluster. A new particle is then launched on the sphere and the process is continued until the required cluster size is reached