Self-organized criticality as an absorbing-state phase transition

TL;DR

This paper links self-organized criticality in sandpile models to phase transitions with absorbing states, showing criticality occurs at zero dissipation and driving parameters, supported by simulations and a new field theory.

Contribution

It demonstrates that self-organized criticality arises from an absorbing-state phase transition with specific parameter conditions, and introduces a field theory coupling the order parameter to energy density.

Findings

Sandpile models are critical only at zero dissipation and driving.

Power-law avalanche distributions are common in models with many absorbing states.

Simulations confirm critical behavior at epsilon=h=0 and fixed energy density.

Abstract

We explore the connection between self-organized criticality and phase transitions in models with absorbing states. Sandpile models are found to exhibit criticality only when a pair of relevant parameters - dissipation epsilon and driving field h - are set to their critical values. The critical values of epsilon and h are both equal to zero. The first is due to the absence of saturation (no bound on energy) in the sandpile model, while the second result is common to other absorbing-state transitions. The original definition of the sandpile model places it at the point (epsilon=0, h=0+): it is critical by definition. We argue power-law avalanche distributions are a general feature of models with infinitely many absorbing configurations, when they are subject to slow driving at the critical point. Our assertions are supported by simulations of the sandpile at epsilon=h=0 and fixed energy density (no drive, periodic boundaries), and of the slowly-driven pair contact process. We formulate a field theory for the sandpile model, in which the order parameter is coupled to a conserved energy density, which plays the role of an effective creation rate.