A new crystal growth model based on a stochastic method under an external field

A new crystal growth model, based on Monte Carlo simulation, is introduced to describe the diffusion-limited aggregation (DLA) with an external force that arises from Lorentz's and/or Coulombic interactions. Specific crystal patterns grown under these external forces are reproduced by a Monte Carlo simulation. In the present multi-purpose model, the basic movement of a particle is a random walk, with different transition probabilities in different directions to represent the effect of the external forces. In some cases, patterns that are qualitatively different from standard DLA clusters are observed, and they are successfully compared with existing experiments and theories.