25 Years of Self-Organized Criticality: Concepts and Controversies

Abstract

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attacted much comment, ranging from the very positive to the polemical. The other papers in this special issue (Aschwanden et al, 2014; McAteer et al, 2014; Sharma et al, 2015) showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak's own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner, 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld's original papers.

52 pages, 3 figures

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• Self-Organized Criticality in Solar and Stellar Flares: Are Extreme Events Scale-Free ?
• Critical neuronal models with relaxed timescales separation
• Self-Organized Criticality and Pattern Emergence through the lens of Tropical Geometry
• Insights into the physics of neutron star interiors from pulsar glitches
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• Effects of Turbulent Environment and Random Noise on Self-Organized Critical Behavior: Universality vs Nonuniversality
• The Emergence of Weak Criticality in SOC systems
• Effects of turbulent environment on self-organized critical behavior: Isotropy vs Anisotropy
• Fractal analyses of networks of integrate-and-fire stochastic spiking neurons
• Self-Organized Higgs Criticality
• Tail of the distribution of fatalities in epidemics
• Ubiquitous order known as chaos
• Controlling excitation avalanches in driven Rydberg gases
• Evolving Powergrids in Self-Organized Criticality: An analogy with Sandpile and Earthquakes
• Adaptation to criticality through organizational invariance in embodied agents
• Description of mesoscale pattern formation in shallow convective cloud fields by using time-dependent Ginzburg-Landau and Swift-Hohenberg stochastic equations
• Renormalization group analysis of a self-organized critical system: Intrinsic anisotropy vs random environment
• $1/x$ Probability Distribution in a Close Proximity of the Bak-Tang-Wiesenfeld Sandpile
• Percolation with trapping mechanism drives active gels to the critically connected state
• Correlation Functions of Photospheric Magnetic Fields in Solar Active Regions
• From Boltzmann to Zipf through Shannon and Jaynes
• A New Approach to Solar Flare Prediction
• Dimensional transmutation and nonconventional scaling behaviour in a model of self-organized criticality
• Can biological quantum networks solve NP-hard problems?
• The Pedagogical Representation of Mass Functions with LEGO and their Origin
• Delegated Causality of Complex Systems
• Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependence
• Emergence of oscillations in fixed energy sandpile models on complex networks
• Expanding and Self-Organizing 2D Universe Models Emerging from Frozen Trivalent Spin Networks
• Measuring complexity
• Criticality Analysis: Bio-inspired Nonlinear Data Representation
• Temperature-activated dislocation avalanches signaling brittle-to-ductile transition in BCC micropillars
• von Karman - Howarth Similarity of Spatial Correlations and the Distribution of Correlation Lengths in Solar Photospheric Turbulence
• Time path of turbulence and multi-fractality of magnetic field in the evolution of an active region
• Nearly Tight Bounds for Sandpile Transience on the Grid
• Forecasting Solar Flares by Data Assimilation in Sandpile Models
• Topological Field Theory and Stochastic Dynamics
• A Spiking Neural Dynamical Drift-Diffusion Model on Collective Decision Making with Self-Organized Criticality
• Ergodic Concepts for a Self-Organizing Trivalent Spin Network: A Path to $(2+1)$-dimensional Black Hole Entropy
• An extension of the Ising-Curie-Weiss model of self-organized criticality with a threshold on the interaction range