Patterned and Disordered Continuous Abelian Sandpile Model

TL;DR

This paper investigates the critical behavior of continuous Abelian sandpile models with anisotropic toppling rules and introduces a new random fixed point in a disordered variant using conformal field theory.

Contribution

It presents a detailed analysis of ordered and disordered continuous Abelian sandpile models, revealing new critical phenomena and fixed points.

Findings

Ordered models produce patterned structures.

Disordered models exhibit a new random fixed point.

Critical properties are characterized using conformal field theory.

Abstract

We study critical properties of the continuous Abelian sandpile model with anisotropies in toppling rules that produce ordered patterns on it. Also we consider the continuous directed sandpile model perturbed by a weak quenched randomness and study critical behavior of the model using perturbative conformal field theory and show the model has a new random fixed point.