Exact solution of stochastic directed sandpile model

Abstract

We introduce and analytically solve a directed sandpile model with stochastic toppling rules. The model clearly belongs to a different universality class from its counterpart with deterministic toppling rules, previously solved by Dhar and Ramaswamy. The critical exponents are D_||=7/4, τ=10/7 in two dimensions and D_||=3/2, τ=4/3 in one dimension. The upper critical dimension of the model is three, at which the exponents apart from logarithmic corrections reach their mean-field values D_||=2, τ=3/2.

4 pages, 2 figures. Added numerical data for 3D case (2nd figure)

References in corpus (3)

• Theoretical Results for Sandpile Models of SOC with Multiple Topplings
• Universality classes in directed sandpile models
• Scale-free energy dissipation and dynamic phase transition in stochastic sandpiles

Cited by in corpus (16)

• Generic Sandpile Models Have Directed Percolation Exponents
• The Asymmetric Avalanche Process
• Confirming and extending the hypothesis of universality in sandpiles
• Large Scale Structures, Symmetry, and Universality in Sandpiles
• Anisotropy and universality: the Oslo model, the rice pile experiment and the quenched Edwards-Wilkinson equation
• Sandpile models and random walkers on finite lattices
• Steady state of Stochastic Sandpile Models
• Exact solution of the totally asymmetric Oslo model
• Directed abelian algebras and their applications to stochastic models
• An Interface View of Directed Sandpile Dynamics
• Directed avalanche processes with underlying interface dynamics
• Emergence and complexity in theoretical models of self-organized criticality
• Relevance of Abelian Symmetry and Stochasticity in Directed Sandpiles
• Multi-Avalanche Correlations in Directed Sandpile Models
• Universality classes and crossover behaviors in non-Abelian directed sandpiles
• A natural stochastic extension of the sandpile model on a graph