The Bak-Tang-Wiesenfeld sandpile model around the upper critical dimension

TL;DR

This paper investigates the Bak-Tang-Wiesenfeld sandpile model across various dimensions, analyzing avalanche behaviors and critical exponents, and confirms mean field behavior above the upper critical dimension with fractal avalanche structures.

Contribution

It provides a detailed finite size scaling analysis of the model in dimensions D>=6, identifying critical exponents and avalanche structures, and confirms theoretical predictions about mean field behavior.

Findings

Exponents match mean field values above D=4

Avalanches are fractal structures above the critical dimension

Finite size scaling yields critical exponents and avalanche dimensions

Abstract

We consider the Bak-Tang-Wiesenfeld sandpile model on square lattices in different dimensions (D>=6). A finite size scaling analysis of the avalanche probability distributions yields the values of the distribution exponents, the dynamical exponent, and the dimension of the avalanches. Above the upper critical dimension D_u=4 the exponents equal the known mean field values. An analysis of the area probability distributions indicates that the avalanches are fractal above the critical dimension.