Phase diagram of diffusion driven aggregate growth in plane: competition of anisotropy and adhesion

Understanding critical properties of non-equilibrium processes [1] is still a challenging problem of contemporary statistical physics. Of particular interest (both theoretical and practical) are the dynamical growth phenomena. The model for the two-dimensional (2D) growth (Diffusion Limited Aggregation) was introduced almost thirty years ago by Witten and Sander [2]. Structures grown by DLA look very similar to those found in nature and society [3], for example, ice crystals on window, mineral dendrites on the surfaces of limestones, colony of bacteria, nano-size crystals grown on the crystal surface, monolayer polymer films, interfaces in Hele-Shaw cell, urban growth, etc. We ask the following questions: are the properties of all above mentioned natural structures the same? Are clusters generated by different models identical or not? The important characteristic of a growth structure is its fractal dimension [4]. According to the universality concept of critical phenomena the value of fractal dimension is one of the characteristics of universality class (see, f.e., ref. [5]). We build clusters with different number n of axes of the anisotropy field, varying from n = 3 to n = 8, as well as off-lattice clusters (this case is equivalent to n→∞). Second parameter of the model is so-called noise reduction level m, which physically could be considered as a quantity, inversely proportional to adhesion. Technically it is a number of collisions of a walking particle with an anisotropy axis before it sticks to the cluster. We use off-lattice killing-free algorithm [7] to generate ensemble of 1000 clusters with the size up to 5 ·107 particles in each cluster for different values of n and m. We do not consider surface tension of the cluster [6]. We obtain effective fractal dimension of the clusters as function of the