Studying Self-Organized Criticality with Exactly Solved Models

Abstract

This is a somewhat expanded version of the notes of a series of lectures given at Lausanne and Stellenbosch in 1998-99. They are intended to provide a pedagogical introduction to the abelian sandpile model of self-organized criticality, and its related models : the q=0 state Potts model, Takayasu aggregation model, the voter model, spanning trees, Eulerian walkers model etc. It provides an overview of the known results, and explains the equivalence of these models. Some open questions are discussed in the concluding section.