Sandpile models in the large

TL;DR

This paper reviews the connection between large-scale properties of critical systems, exemplified by 2D Abelian sandpile models, and their field theory descriptions, highlighting how various observables match theoretical predictions.

Contribution

It provides a detailed review of how the large-scale behavior of Abelian sandpile models corresponds to field theory, including boundary conditions and dissipation effects.

Findings

Bulk and boundary height variables match field theory predictions

Spanning tree observables are consistent with the field theoretic description

Boundary conditions and dissipation are effectively incorporated in the field theory

Abstract

This contribution is a review of the deep and powerful connection between the large scale properties of critical systems and their description in terms of a field theory. Although largely applicable to many other models, the details of this connection are illustrated in the class of two-dimensional Abelian sandpile models. Bulk and boundary height variables, spanning tree related observables, boundary conditions and dissipation are all discussed in this context and found to have a proper match in the field theoretic description.