Logarithmic conformal invariance in the Abelian sandpile model

TL;DR

This paper reviews the Abelian sandpile model as a promising lattice realization of logarithmic conformal invariance with central charge -2, supported by boundary condition analysis, correlation calculations, and dissipation considerations.

Contribution

It provides a comprehensive review of evidence linking the Abelian sandpile model to logarithmic conformal field theories, highlighting new insights into boundary conditions and dissipation effects.

Findings

Evidence of conformal invariance in boundary conditions

Correlation functions of height variables match theoretical predictions

Dissipation plays a key role in understanding logarithmic features

Abstract

We review the status of the two-dimensional Abelian sandpile model as a strong candidate to provide a lattice realization of logarithmic conformal invariance with central charge c=-2. Evidence supporting this view is collected from various aspects of the model. These include the study of some conformally invariant boundary conditions, and the corresponding boundary condition changing fields, the calculation of correlations of certain bulk and boundary observables (the height variables) as well as a proper account of the necessary dissipation, which allows for a physical understanding of some of the strange but generic features of logarithmic theories.