Conformal field theory correlations in the Abelian sandpile mode

TL;DR

This paper computes all multipoint correlation functions of local bond modifications in the 2D Abelian sandpile model, confirming their relation to logarithmic conformal field theory and providing explicit formulas and boundary effects.

Contribution

It provides the first complete calculation of correlation functions for all local bond modifications in the Abelian sandpile model, linking them to logarithmic CFT with explicit coefficients.

Findings

All local bond modifications have scaling dimension two.

Correlation functions can be expressed as linear combinations of operators in LCFT.

Explicit formulas for coefficients and boundary effects are derived.

Abstract

We calculate all multipoint correlation functions of all local bond modifications in the two-dimensional Abelian sandpile model, both at the critical point, and in the model with dissipation. The set of local bond modifications includes, as the most physically interesting case, all weakly allowed cluster variables. The correlation functions show that all local bond modifications have scaling dimension two, and can be written as linear combinations of operators in the central charge -2 logarithmic conformal field theory, in agreement with a form conjectured earlier by Mahieu and Ruelle in Phys. Rev. E 64, 066130 (2001). We find closed form expressions for the coefficients of the operators, and describe methods that allow their rapid calculation. We determine the fields associated with adding or removing bonds, both in the bulk, and along open and closed boundaries; some bond defects have scaling dimension two, while others have scaling dimension four. We also determine the corrections to bulk probabilities for local bond modifications near open and closed boundaries.