Spatial Asymmetric Two dimensional Continuous Abelian Sandpile Model

TL;DR

This paper introduces asymmetric variations of the continuous Abelian sandpile model, analyzing their probability distributions and deriving the corresponding field theories to understand their behavior.

Contribution

It presents novel asymmetric continuous Abelian sandpile models with directedness and ellipticity, along with their probability distributions and associated field theories.

Findings

Probability distributions of heights are characterized.

Field theories corresponding to the asymmetric models are derived.

Fields associated with specific height variables are identified.

Abstract

We insert some asymmetries in the continuous Abelian sandpile models, such as directedness and ellipticity. We analyze probability distribution of different heights and also find the field theory corresponding to the models. Also we find the fields associated with some height variables.