Introduction to the Sandpile Model

Abstract

This article is based on a talk given by one of us (EVI) at the conference ``StatPhys-Taipei-1997''. It overviews the exact results in the theory of the sandpile model and discusses shortly yet unsolved problem of calculation of avalanche distribution exponents. The key ingredients include the analogy with the critical reaction-diffusion system, the spanning tree representation of height configurations and the decomposition of the avalanche process into waves of topplings.

References in corpus (1)

• Avalanches and Waves in the Abelian Sandpile Model

Cited by in corpus (31)

• The abelian sandpile and related models
• Size distributions of shocks and static avalanches from the Functional Renormalization Group
• Scaling fields in the two-dimensional abelian sandpile model
• Statistics of static avalanches in a random pinning landscape
• Avalanche dynamics of elastic interfaces
• A c=-2 boundary changing operator for the Abelian sandpile
• Avalanche shape and exponents beyond mean-field theory
• Generic Sandpile Models Have Directed Percolation Exponents
• The raise and peel model of a fluctuating interface
• Logarithmic scaling for height variables in the Abelian sandpile model
• Pre-logarithmic and logarithmic fields in a sandpile model
• Infinite volume limit of the Abelian sandpile model in dimensions d >= 3
• Limiting shapes for deterministic centrally seeded growth models
• Stabilizability and percolation in the infinite volume sandpile model
• Pair correlations in sandpile model: a check of logarithmic conformal field theory
• Critical Behavior of Sandpile Models with Sticky Grains
• Exact integration of height probabilities in the Abelian Sandpile Model
• Approaching criticality via the zero dissipation limit in the abelian avalanche model
• Granular Matter: a wonderful world of clusters in far-from-equilibrium systems
• A probabilistic approach to Zhang's sandpile model
• Probability distribution of residence times of grains in models of ricepiles
• Directed nonabelian sandpile models on trees
• Probability distribution of residence-times of grains in sandpile models
• Scaling of avalanche queues in directed dissipative sandpiles
• The Ising model in a Bak-Tang-Wiesenfeld sandpile
• A general method for calculating lattice Green functions on the branch cut
• Deterministic Abelian Sandpile and square-triangle tilings
• The Potts model built on sand
• A stochastic theory for temporal fluctuations in self-organized critical systems
• Spatial Asymmetric Two dimensional Continuous Abelian Sandpile Model
• Emergence of quasi-units in the one dimensional Zhang model