Paths to Self-Organized Criticality

TL;DR

This paper provides a comprehensive overview of self-organized criticality (SOC), detailing its theoretical foundations, different pathways to emergence, and current experimental status, emphasizing the connection with nonequilibrium phase transitions.

Contribution

It introduces multiple pathways to SOC from critical points, including absorbing-state transitions and driven systems, and reviews experimental realizations and theoretical models.

Findings

SOC arises from slow driving in systems with absorbing-state phase transitions.

Multiple pathways to SOC include extremal dynamics and driving at near-zero rates.

Experimental realizations of SOC are discussed in context of theoretical models.

Abstract

We present a pedagogical introduction to self-organized criticality (SOC), unraveling its connections with nonequilibrium phase transitions. There are several paths from a conventional critical point to SOC. They begin with an absorbing-state phase transition (directed percolation is a familiar example), and impose supervision or driving on the system; two commonly used methods are extremal dynamics, and driving at a rate approaching zero. We illustrate this in sandpiles, where SOC is a consequence of slow driving in a system exhibiting an absorbing-state phase transition with a conserved density. Other paths to SOC, in driven interfaces, the Bak-Sneppen model, and self-organized directed percolation, are also examined. We review the status of experimental realizations of SOC in light of these observations.