Multi-Avalanche Correlations in Directed Sandpile Models

TL;DR

This paper investigates the correlations between multiple avalanches in directed sandpile models, revealing a universal behavior in two-avalanche distributions linked to particle conservation.

Contribution

It demonstrates that despite differences in single avalanche exponents, the two-avalanche distribution exhibits universal exponents across models due to particle conservation.

Findings

Two-avalanche exponents are identical across models.

Single avalanche exponents differ among models.

Universality is rooted in particle conservation.

Abstract

Multiple avalanches, initiated by simultaneously toppling neighbouring sites, are studied in three different directed sandpile models. It is argued that, while the single avalanche exponents are different for the three models, a suitably defined two-avalanche distribution has identical exponents. The origin of this universality is traced to particle conservation.