1999/04/30 by Barbara Drossel · 1 citation
Earth and Planetary Sciences · Environmental Science · Mathematics · Physics and Astronomy · #Abelian sandpile model #Geological formations and processes #Geometry #Landslides and related hazards #Mathematics #Physics #Scaling #Statistical physics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.61.r2168
4 pages, 5 figures; the new version takes into account that the radius distribution of avalanches cannot become steeper than a certain power law
arxiv created 1999/05/18 · openalex publication_date 2000/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Abelian sandpile model in two dimensions does not show the type of critical behavior familiar 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/√(r) to reach the boundary. As a consequence, the scaling behavior of the model can be obtained from evaluating dissipative avalanches alone, allowing one not only to determine the values of all exponents, but showing also the breakdown of finite-size scaling.