Temperature scaling, glassiness and stationarity in the Bak-Sneppen model |
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Authors: | D Head |
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Institution: | (1) Department of Physics and Astronomy, JCMB King's Buildings, University of Edinburgh, Edinburgh EH9 3JZ, UK, GB |
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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 (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.
Received 14 January 2000 and Received in final form 18 April 2000 |
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Keywords: | PACS 05 40 -a Fluctuation phenomena random processes noise and Brownian motion - 05 65 +b Self-organized systems - 45 70 Ht Avalanches |
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