Boundary height fields in the Abelian sandpile model

TL;DR

This paper investigates boundary height correlations in the Abelian sandpile model by analyzing a dissipative extension, revealing they correspond to a massive perturbation of a c=-2 logarithmic conformal field theory.

Contribution

It identifies the boundary height fields in the dissipative Abelian sandpile model as a massive perturbation of a c=-2 logarithmic conformal field theory, providing a new theoretical understanding.

Findings

Boundary height variables are described by a massive c=-2 LCFT.

The dissipative extension facilitates the analysis of boundary correlations.

Boundary height fields correspond to a massive perturbation of the LCFT.

Abstract

We study the abelian sandpile model on the upper half plane, and reconsider the correlations of the four height variables lying on the boundary. For more convenience, we carry out the analysis in the dissipative (massive) extension of the model and identify the boundary scaling fields corresponding to the four heights. We find that they all can be accounted for by the massive pertubation of a c=-2 logarithmic conformal field theory.