2008/06/30 by Juan A. Bonachela, Miguel A. Muñoz, Miguel A. Munoz · 40 citations
Earth and Planetary Sciences · Environmental Science · Mathematics · Physics and Astronomy · #Abelian sandpile model #Algorithm #Cellular automaton #Conservation law #Critical exponent #Criticality #Directed percolation #Geological formations and processes #Geometry #Groundwater flow and contamination studies #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Renormalization group #Scaling #Statistical physics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.78.041102
published in Physical Review E 78(4), 041102 (American Physical Society) · 6 Figures.9 pages
openalex publication_date 2008/10/01 · arxiv created 2008/10/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Stochastic sandpiles self-organize to an absorbing-state critical point with scaling behavior different from directed percolation (DP) and characterized by the presence of an additional conservation law. This is usually called the C-DP or Manna universality class. There remains, however, an exception to this universality principle: a sandpile automaton introduced by Maslov and Zhang, which was claimed to be in the DP class despite the existence of a conservation law. We show, by means of careful numerical simulations as well as by constructing and analyzing a field theory, that (contrarily to what was previously thought) this sandpile is also in the C-DP or Manna class. This confirms the hypothesis of universality for stochastic sandpiles and gives rise to a fully coherent picture of self-organized criticality in systems with conservation. In passing, we obtain a number of results for the C-DP class and introduce a strategy to easily discriminate between DP and C-DP scaling.