Abstract
We introduce a renormalization scheme of novel type that allows us to characterize the critical state and the scale invariant dynamics in sandpile models. The attractive fixed point clarifies the nature of self-organization in these systems. Universality classes can be identified and the critical exponents can be computed analytically. We obtain tau = 1.253 for the avalanche exponent and z = 1.234 for the dynamical exponent. These results are in good agreement with computer simulations. The method can be naturally extended to other problems with nonequilibrium stationary states.
Keywords
sandpile models, self-organization
Subject Categories
Renormalization (Physics)
Disciplines
Physics
Publisher
American Physical Society
Publication Date
3-14-1994
Rights Information
©1994 American Physical Society
Rights Holder
American Physical Society
Permanent URL
Recommended Citation
Pietronero, L; Vespignani, A; and Zapperi, S, "Renormalization scheme for self-organized criticality in sandpile models" (1994). Physics Faculty Publications. Paper 227. http://hdl.handle.net/2047/d20002187
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Notes
Originally published in Physical Review Letters, v.72 no.11 (1994), pp.1690-1693. DOI:10.1103/PhysRevLett.72.1690. Dr. Vespignani is affiliated with Northeastern University as of the time of deposit.