Phase transition in diffusion-limited aggregation with two immiscible components

A diffusion-limited-aggregation (DLA) model with two immiscible components (A and B atoms) is presented to investigate a phase transition in morphological changes. A segregation occurs where the DLA pattern is constructed by a mixture of trees consisting of only A atoms and trees consisting of only B atoms. Above a critical concentration ${\mathit{p}}_{\mathit{c}}$, trees with only A atoms exceed trees with only B atoms, and the DLA with only A atoms dominates. It is found that a phase transiton between A-DLA and B-DLA occurs at the critical concentration ${\mathit{p}}_{\mathit{c}}$, where A-DLA and B-DLA represent, respectively, DLA with only A atoms and DLA with only B atoms. The phase transition is analyzed by making use of the real-space renormalization-group method. The correlation length ξ scales as ξ≊(p-${\mathit{p}}_{\mathit{c}}$${)}^{\mathrm{-}\nu }$, where ${\mathit{p}}_{\mathit{c}}$=0.5 and ν=1.85 on the square lattice.