Numerical Determination of the Avalanche Exponents of the Bak-Tang-Wiesenfeld Model

TL;DR

This paper accurately determines the avalanche exponents of the Bak-Tang-Wiesenfeld sandpile model using a new analysis method that minimizes finite-size effects, providing refined estimates that differ slightly from previous approaches.

Contribution

It introduces a novel data analysis technique to improve the precision of avalanche exponent measurements in the sandpile model.

Findings

Exponents differ slightly from previous measurements.

New method reduces finite-size effects.

Provides more accurate avalanche distribution exponents.

Abstract

We consider the Bak-Tang-Wiesenfeld sandpile model on a two-dimensional square lattice of lattice sizes up to L=4096. A detailed analysis of the probability distribution of the size, area, duration and radius of the avalanches will be given. To increase the accuracy of the determination of the avalanche exponents we introduce a new method for analyzing the data which reduces the finite-size effects of the measurements. The exponents of the avalanche distributions differ slightly from previous measurements and estimates obtained from a renormalization group approach.