AUTHOR=Ruelle Philippe TITLE=Sandpile Models in the Large JOURNAL=Frontiers in Physics VOLUME=9 YEAR=2021 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.641966 DOI=10.3389/fphy.2021.641966 ISSN=2296-424X 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.