Self-organized criticality and directed percolation
Abstract
A sandpile model with a stochastic toppling rule is studied. The control parameters and the phase diagram are determined through a mean-field approach, and the subcritical and critical regions are analysed. The model is found to have some similarities with directed percolation, but the existence of different boundary conditions and conservation law leads to a different universality class, where the critical state is extended to a line segment due to self-organization. These results are supported by numerical simulations in one dimension. This model constitutes a simple model which captures the essential difference between ordinary nonequilibrium critical phenomena, like directed percolation, and self-organized criticality.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- April 1999
- DOI:
- 10.1088/0305-4470/32/14/004
- arXiv:
- arXiv:cond-mat/9810408
- Bibcode:
- 1999JPhA...32.2633V
- Keywords:
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- Condensed Matter
- E-Print:
- 9 pages, 10 eps figs, revtex, submitted to J. Phys. A