On the scaling behavior of the abelian sandpile model

Abstract

The abelian sandpile model in two dimensions does not show the type of critical behavior familar from equilibrium systems. Rather, the properties of the stationary state follow from the condition that an avalanche started at a distance r from the system boundary has a probability proportional to 1/sqrt(r) to reach the boundary. As a consequence, the scaling behavior of the model can be obtained from evaluating dissipative avalanches alone, allowing not only to determine the values of all exponents, but showing also the breakdown of finite-size scaling.

4 pages, 5 figures; the new version takes into account that the radius distribution of avalanches cannot become steeper than a certain power law

References in corpus (2)

• Multifractal scaling in the Bak-Tang-Wiesenfeld Sandpile and edge events
• Scaling of waves in the Bak-Tang-Wiesenfeld sandpile model

Cited by in corpus (11)

• Power laws and Self-Organized Criticality in Theory and Nature
• Evolution in complex systems
• Critical behavior of a one-dimensional fixed-energy stochastic sandpile
• Quenched noise and over-active sites in sandpile dynamics
• Theoretical Results for Sandpile Models of SOC with Multiple Topplings
• Avalanche exponents and corrections to scaling for a stochastic sandpile
• The self-organized critical forest-fire model on large scales
• Critical behavior and conservation in directed sandpiles
• Dissipative stochastic sandpile model on small world network : properties of non-dissipative and dissipative avalanches
• Fine Structure of Avalanches in the Abelian Sandpile Model
• Absorbing phase transitions in a non-conserving sandpile model