Temperature scaling, glassiness and stationarity in the Bak-Sneppen model
Department of Physics and Astronomy, JCMB King's Buildings,
University of Edinburgh, Edinburgh EH9 3JZ, UK
Revised: 18 April 2000
Published online: 15 September 2000
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 (J. Phys. I France 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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.65.+b – Self-organized systems / 45.70.Ht – Avalanches
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000