Temperature scaling, glassiness and stationarity in the Bak-Sneppen model

TL;DR

This paper investigates the critical behavior of the Bak-Sneppen model, revealing hierarchical timescales, deriving scaling exponents, relating it to glass models, and proposing a new definition of self-organised criticality.

Contribution

It introduces a hierarchical timescale perspective, derives critical exponents numerically, connects the model to glassy systems, and proposes a new general definition of self-organised criticality.

Findings

Criticality corresponds to separation of timescales.

Scaling relations with derived exponents near criticality.

Relation of Bak-Sneppen model to glass models.

Abstract

We show that the emergence of criticality in the locally-defined Bak-Sneppen model corresponds to separation over a hierarchy of timescales. Near to the critical point the model obeys scaling relations, with exponents which we derive numerically for a one-dimensional system. We further describe how the model can be related to the glass model of Bouchaud [{\em J. Phys. I France {\bf 2}, 1705 (1992)}], and we use this insight to comment on the usual assumption of stationarity in the Bak-Sneppen model. Finally, we propose a general definition of self-organised criticality which is in partial agreement with other recent definitions.