Competition between two kinds of entities in a Diffusion—Limited Aggregration process

Abstract

An extra degree of freedom (the “spin”) is added in the well-known Diffusion-Limited Aggregation growth model. A physically relevant coupling energy between aggregating spins in presence of an external magnetic field is defined. This model generates a kinetic growth competition between two kinds of entities and leads to a wide variety of kinetic processes and morphologies distributed in the “phase diagram” of the two growth parameters (coupling and field). Out of the cluster, the motion of the spins is still Brownian. The process leads to cluster fractal structures with fractal dimensions varying from 1.68±0.02 to 1.99±0.01 depending on the coupling parameters. Some physical ideas are presented in order to describe the new kinetic processes. Beside geometrical properties of the clusters, physical properties were also measured. For finite size clusters, a “transition” in the magnetization occurs at fixed (βJ, βH)_c values. This “transition” shows that a species can dominate the other in finite clusters. Moreover, the fractal dimension of the clusters drastically drops at the same critical values. These behaviours are interestingly new and unexpected.