Pair correlations in sandpile model: a check of logarithmic conformal field theory

TL;DR

This paper calculates height variable correlations in the 2D Abelian sandpile model, confirming the logarithmic conformal field theory predictions for the dominant correlation behavior.

Contribution

It extends previous results by including cases where one height exceeds the minimal value, verifying the logarithmic conformal field theory predictions.

Findings

Correlation log r/r^4 matches theoretical predictions

Extension of known correlations to larger height variables

Confirmation of logarithmic conformal field theory in sandpile models

Abstract

We compute the correlations of two height variables in the two-dimensional Abelian sandpile model. We extend the known result for two minimal heights to the case when one of the heights is bigger than one. We find that the most dominant correlation log r/r^4 exactly fits the prediction obtained within the logarithmic conformal approach.