PHASE-TRANSITION IN DIFFUSION-LIMITED AGGREGATION WITH 2 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 p(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 p(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 xi scales as xi almost-equal-to (p-p(c))-v, where p(c) = 0.5 and v = 1.85 on the square lattice.