Paths to self-organized criticality

TLDR

Several paths lead from a conventional critical point to self‑organized criticality, including driven interfaces, the Bak‑Sneppen model, and self‑organized directed percolation. The paper introduces SOC pedagogically, explores its links to nonequilibrium phase transitions, and reviews experimental realizations. The authors describe SOC as emerging from absorbing‑state phase transitions, such as directed percolation, and show how supervision or driving—via extremal dynamics or vanishing‑rate driving—induces criticality, while also reviewing experimental realizations. In sandpile models, SOC arises from slow driving in a system with an absorbing‑state phase transition and a conserved density.

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.