Sandpiles with finite-range interactions

Abstract We investigate the sandpile model with Yukawa-type interactions, whose effective range is tuned by an external parameter R . Our results reveal that at specific values of R , the system exhibits percolating avalanches that span the system, leading to percolation. The percolation probability demonstrates two distinct regimes as a function of R : for sufficiently small R , it increases monotonically, while for large R it shows intermittent behavior in terms of R , accompanied with some abrupt jumps. We refer to these as pseudo-percolation transitions , based on which we propose a hierarchical percolation model at the mean-field level. We further examine both local and global geometrical observables. The local quantities include avalanche size, mass, and duration and sub-avalanche mass, while for the global characterization we analyze the loop length and gyration radius of the external perimeter, as well as the mass of sub-avalanches, defined as the connected components within a total avalanche. Remarkably, the distribution functions of these observables exhibit power-law scaling behavior for all values of R , with exponents that vary systematically with R . Notably, in the vicinity of the pseudo-percolation transition points, the exponents approach characteristic values, signaling a distinct critical behavior.