Growth model with phase transition: Drift-diffusion-limited aggregation

A growth model is presented to show a phase transition. The drift-diffusion-limited aggregation model with a positive drift proposed by Meakin [Phys. Rev. B 28, 5221 (1983)] is extended to that with a negative drift. When the drift changes from a positive value to a negative value, the structure of the aggregate varies from a dense structure, through the diffusion-limited aggregation (DLA) fractal, to a needlelike structure. In contrast with the crossover from the DLA fractal to the dense structure at a positive drift, at a negative drift the crossover is shown from the fractal structure at short length scales to a one-dimensional structure at longer length scales.