Self-Organised Criticality Theory, Models and Characterisation

"When Bak, Tang, and Wiesenfeld (1987) coined the term Self-Organised Criticality (SOC), it was an explanation for an unexpected observation of scale invariance and at the same time, a programme of further research. Over the years it developed into a subject area which is concerned mostly with the analysis of computer models that display a form of generic scale invariance. The primacy of the computer model is manifest in the first publication and throughout the history of SOC, which evolved with and revolved around such computer models. That has led to a plethora of computer 'models', many of which are not intended to model much except themselves (also Gisiger, 2001), in the hope that they display a certain aspect of SOC in a particularly clear way. The question whether SOC exists is empty if SOC is merely the title for a certain class of computer models. In the following, the term SOC will therefore be used in its original meaning (Bak et al, 1987), to be assigned to systems with spatial degrees of freedom [which] naturally evolve into a self-organized critical point. Such behaviour is to be juxtaposed to the traditional notion of a phase transition, which is the singular, critical point in a phase diagram, where a system experiences a breakdown of symmetry and long-range spatial and in non-equilibrium, also temporal correlations, generally summarised as (power law) scaling (Widom, 1965a,b; Stanley, 1971)"--Publisher.