Why patchy diffusion-limited aggregation belongs to the directed-percolation universality class

We present a possible link between nonequilibrium phase transition observed in patchy diffusion-limited aggregation (DLA) [M. J. Kartha and A. Sayeed, Phys. Lett. A 380, 2791 (2016)10.1016/j.physleta.2016.06.036] and directed bond percolation (DP). A system of directed percolation with patchy particles (patchy DP) in which the bond connectivity is established depending on patch size p is analyzed. It is observed that patchy DP starting from a single seed shows a nonequilibrium phase transition. Below a critical value of the patch size pc, the system reaches an absorbing state above which is a fluctuating active state as observed in the DP system. The value of this nonuniversal parameter pc is observed to be slightly higher than the value observed in patchy DLA. Close to the critical value, the order parameter P(∞)∼(p-pc)β where β=0.272±0.010, which is consistent with the directed-percolation universality class. Therefore the intrinsic nature of patchy DP is responsible for the phase transition in patchy DLA. This study reveals that the estimated critical value of patch size pc=0.80625±0.00020 in patchy DP is different from the critical bond probability pc=0.6447 in the DP system. This elucidates that the bond probability in DP is not equivalent to the patch probability of a particular site. Our work also gives an insight into the problem related with formation of an extended network of pentagon subunits in connection with the virus capsid.