Rare events and breakdown of simple scaling in the Abelian sandpile model

1998/05/31 by Mario De Menech, M. De Menech, Attilio L. Stella +3 · 112 citations
Economics, Econometrics and Finance · Materials Science · Mathematics · Physics and Astronomy · #Abelian group #Abelian sandpile model #Complex Systems and Time Series Analysis #Constant (computer programming) #Fractal #Geometry #Intermittency #Limit (mathematics) #Material Dynamics and Properties #Mathematical analysis #Mathematics #Mechanics #Multifractal system #Physics #Pure mathematics #Scaling #Simple (philosophy) #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.58.r2677

published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 58(3), R2677-R2680 (American Physical Society) · RevTex, 4 Pages, 2 Figures

arxiv created 1998/07/16 · openalex publication_date 1998/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Due to intermittency and conservation, the Abelian sandpile in two dimensions obeys multifractal, rather than finite size scaling. In the thermodynamic limit, a vanishingly small fraction of large avalanches dominates the statistics and a constant gap scaling is recovered in higher moments of the toppling distribution. Thus, rare events shape most of the scaling pattern and preserve a meaning for effective exponents, which can be determined on the basis of numerical and exact results.

Citations

• Polymers and percolation in two dimensions and twisted N = 2 supersymmetry

Cited by

• The Abelian sandpile and related models
• Scaling behavior of the Abelian sandpile model
• Critical behavior of a one-dimensional fixed-energy stochastic sandpile
• Randomness and a step-like distribution of pile heights in avalanche models