1994/09/16 by Hans-Martin Broeker, H.-M Bröker, Peter Grassberger +1 · 1 citation
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1209/0295-5075/30/6/001
11 pages, NLATEX
arxiv created 1994/09/16 · openalex publication_date 1995/05/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We point out a new mechanism which can lead to mean-field-type behaviour in non-equilibrium critical phenomena. We demonstrate this mechanism on a two-dimensional model which can be understood as a stochastic and non-conservative version of the Abelian sandpile model of Bak et al. ( Phys. Rev. Lett. , 59 (1987) 381). This model has a second-order phase transition whose critical behaviour seems at least partly described by the mean-field approximation for percolation, in spite of the low dimension and the fact that all interactions are of short range. Furthermore, the approximation obtained by replacing the lattice by a Bethe tree is very precise in the entire range of the control parameter.