Studying Self-Organized Criticality with Exactly Solved Models

TL;DR

This paper provides a pedagogical overview of self-organized criticality through exactly solvable models, including the abelian sandpile and related models, highlighting their known results and equivalences.

Contribution

It offers a comprehensive introduction to exactly solved models of self-organized criticality and discusses their interrelations and open questions.

Findings

Overview of known results in self-organized criticality models

Explanation of model equivalences

Discussion of open research questions

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.