Emergent spatial structures in critical sandpiles

TL;DR

This paper introduces a new directed sandpile model with stochastic rules, demonstrating how local dynamics and conservation laws produce emergent spatial structures and power-law density tails, with scaling exponents linked to directed percolation.

Contribution

The study presents a novel directed sandpile model with threshold and stochastic toppling, connecting avalanche scaling exponents to directed percolation critical exponents across dimensions.

Findings

Spatial structures emerge in the steady state.

Density exhibits a power-law tail away from the top.

Avalanche distributions scale with directed percolation exponents.

Abstract

We introduce and study a new directed sandpile model with threshold dynamics and stochastic toppling rules. We show that particle conservation law and the directed percolation-like local evolution of avalanches lead to the formation of a spatial structure in the steady state, with the density developing a power law tail away from the top. We determine the scaling exponents characterizing the avalanche distributions in terms of the critical exponents of directed percolation in all dimensions.