Numerical renormalization-group approach to a sandpile.
Multiple topplings and grain redistribution are two essential features in sandpile dynamics. A renormalization group (RG) approach incorporating these features is investigated. The full enumeration of all relaxations involving such an approach is difficult. Instead, we developed an efficient procedure to sample the relaxations. We applied this RG scheme to a square lattice and a triangular lattice. As shown by the fixed point analysis on a square lattice, the effect of multiple topplings leads the resultant height probabilities towards the exact solution while the effect of grain redistribution does not.
Lin
Chai-Yu
CY
Department of Physics, National Chung Cheng University, Chia-Yi 66117, Taiwan.
Cheng
An-Chung
AC
Liaw
Tsong-Ming
TM