Driving sandpiles to criticality and beyond

Abstract

A popular theory of self-organized criticality relates driven dissipative systems to systems with conservation. This theory predicts that the stationary density of the abelian sandpile model equals the threshold density of the fixed-energy sandpile. We refute this prediction for a wide variety of underlying graphs, including the square grid. Driven dissipative sandpiles continue to evolve even after reaching criticality. This result casts doubt on the validity of using fixed-energy sandpiles to explore the critical behavior of the abelian sandpile model at stationarity.

v4 adds reference

References in corpus (2)

• Confirming and extending the hypothesis of universality in sandpiles
• Stabilizability and percolation in the infinite volume sandpile model

Cited by in corpus (12)

• Self-Organized Bistability Associated With First-Order Phase Transitions
• Feedback mechanisms for self-organization to the edge of a phase transition
• The approach to criticality in sandpiles
• Multiple and inverse topplings in the Abelian Sandpile Model
• Numerical Study of the Correspondence Between the Dissipative and Fixed Energy Abelian Sandpile Models
• Sandpiles on the square lattice
• Exact integration of height probabilities in the Abelian Sandpile Model
• Dynamic correlations in the conserved Manna sandpile
• Cut-off for sandpiles on tiling graphs
• The spectrum of the abelian sandpile model
• Critical Density of the Abelian Manna Model via a Multi-type Branching Process
• The hockey-stick conjecture for activated random walk