Sandpile Models

Abstract In this chapter we discuss deterministic and stochastic sandpile models. The relative simplicity of sandpile models has stimulated a series of theoretical approaches and we review here the most successful ones. As in standard critical phenomena the simplest qualitative approach is provided by mean-field theory. A particularly instructive analogy in this respect is provided by branching processes that can be seen as a general mean-field description of avalanche propagation. In the context of sandpile models, branching processes can also be used to describe the role of boundary dissipation on self-organization. While mean-field theory is general but approximate, some properties of sandpile models can be obtained exactly thanks to the Abelian properties of some sandpile models. Finally, we discuss field theory approach to sandpile models and the relation with absorbing state phase transitions.