The Abelian Sandpile Model
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It has been more than 20 years since Bak, Tang and Wiesenfeld’s landmark papers on self-organized criticality (SOC) appeared . The concept of self-organized criticality has been invoked to describe a large variety of different systems. We shall describe the model object of our interest: the Abelian Sandpile Model (ASM). The sandpile model was first proposed as a paradigm of SOC and it is certainly the simplest, and best understood, theoretical model of SOC: it is a non-equilibrium system, driven at a slow steady rate, with local threshold relaxation rules, which shows in the steady state relaxation events in bursts of a wide range of sizes, and long-range spatio-temporal correlations. The ASM consists of a special subclass of the sandpile models that exhibits, in the way we will discuss later, the mathematical structure of an abelian group, and its statistics is connected to that of spanning trees on the relative graph.
KeywordsAbelian Sandpile Model (ASM) Sandbox Long-range Spatiotemporal Correlations Slow Steady Rate Self-organized Criticality (SOC)
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