Higher Order and boundary Scaling Fields in the Abelian Sandpile Model

TL;DR

This paper investigates the Abelian Sandpile Model's boundary effects and higher order corrections to conformal fields, advancing the understanding of self-organized criticality through a field theoretical approach.

Contribution

It derives the first corrections to conformal fields in the ASM considering non-zero lattice parameters and boundary conditions, providing new insights into its field theory description.

Findings

Derived first corrections to conformal fields in ASM

Analyzed effects of non-zero lattice parameters

Studied boundary influences on conformal fields

Abstract

The Abelian Sandpile Model (ASM) is a paradigm of self-organized criticality (SOC) which is related to $c=-2$ conformal field theory. The conformal fields corresponding to some height clusters have been suggested before. Here we derive the first corrections to such fields, in a field theoretical approach, when the lattice parameter is non-vanishing and consider them in the presence of a boundary.