2001/01/24 by Ronald Dickman, Mikko Alava, Mikko J. Alava +6
Materials Science · Mathematics · Physics and Astronomy · #Abelian sandpile model #Condensed matter physics #Critical exponent #Critical point (mathematics) #Directed percolation #Geometry #Material Dynamics and Properties #Mathematical analysis #Mathematical physics #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Phase transition #Physics #Renormalization group #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.64.056104
published as Phys. Rev. E64, 056104 (2001) · 15 pages, 11 figures
arxiv created 2001/01/24 · openalex publication_date 2001/10/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a one-dimensional fixed-energy version (that is, with no input or loss of particles) of Manna's stochastic sandpile model. The system has a continuous transition to an absorbing state at a critical value of the particle density, and exhibits the hallmarks of an absorbing-state phase transition, including finite-size scaling. Critical exponents are obtained from extensive simulations, which treat stationary and transient properties, and an associated interface representation. These exponents characterize the universality class of an absorbing-state phase transition with a static conserved density in one dimension; they differ from those expected at a linear-interface depinning transition in a medium with point disorder, and from those of directed percolation.