Higher order and boundary scaling fields in the Abelian sandpile model

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.

Continuous Abelian Sandpile Model in Two Dimensional Lattice

“…[6]. There are many other analytical results, among them one can mention the results on boundary correlations of height variables and effect of boundary conditions [7,8,9,10,11,12], on presence of dissipation in the model [9,10,13], on field theoretical approaches [17,9,14,15,18], on finite size corrections [11,5] and many other results [3].…”

The spatial asymmetric two-dimensional continuous Abelian sandpile model

“…The probabilities of other one-site clusters with height above one were computed in [6]. There are many other analytical results, among them one can mention the results on boundary correlations of height variables and the effect of boundary conditions [7][8][9][10][11][12], the presence of dissipation in the model [9,10,13], field theoretical approaches [9,[14][15][16][17], finite size corrections [5,11] and many other results [3].…”