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

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

1999-10-14

arxiv.org/abs/cond-mat/9910207v2

Physics

Condensed Matter

Statistical Mechanics

5 pages, 4 figures; differences to previous work clarified. To appear in EPJB

Scientific paper

10.1007/s100510070143

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.

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