Precise toppling balance, quenched disorder, and universality for sandpiles

TL;DR

This paper investigates how the symmetry of toppling matrices in sandpile models influences their universality class, revealing that precise toppling balance determines whether the system exhibits BTW multiscaling or Manna simple scaling.

Contribution

It introduces a sandpile model with quenched random toppling matrices that captures different universality classes based on toppling balance symmetry.

Findings

Symmetric matrices lead to BTW multiscaling universality.

Asymmetric matrices exhibit Manna simple scaling.

Toppling balance determines the universality class.

Abstract

A single sandpile model with quenched random toppling matrices captures the crucial features of different models of self-organized criticality. With symmetric matrices avalanche statistics falls in the multiscaling BTW universality class. In the asymmetric case the simple scaling of the Manna model is observed. The presence or absence of a precise toppling balance between the amount of sand released by a toppling site and the total quantity the same site receives when all its neighbors topple once determines the appropriate universality class.