Connections Between Self-Organised' and Classical' Criticality

#### R. Meester, C. Quant

2005, v.11, Issue 2, 355-370

ABSTRACT

We investigate the nature of the self-organised critical behaviour in the Abelian sandpile model and in the Bak - Sneppen evolution model. We claim that in either case, the self-organised critical behaviour can be explained by the careful choice of the details of the model: they are designed in such a way that the models are necessarily attracted to the critical point of a conventional parametrised equilibrium system. In the case of the Abelian sandpile we prove this connection to conventional criticality rigorously in one dimension, and provide evidence for a similar result in higher dimensions. In the case of the Bak - Sneppen evolution model, we give an overview of the current results, and explain why these results support our claim. We conclude that the term self-organised criticality is somewhat confusing, since the tuning of parameters in a model has been replaced by the careful choice of a suitable model. Viewed as such, we can hardly call this critical behaviour spontaneous.

Keywords: self-organised criticality,Bak - Sneppen evolutionmodel,Abelian sandpile,classical criticality,particle system