Symmetries and Universality Classes in Conservative Sandpile Models

TL;DR

This paper investigates how symmetry properties influence the critical behavior and universality classes in conservative sandpile models, identifying key classes based on abelian and stochastic characteristics.

Contribution

It introduces a comprehensive set of sandpile models with various symmetry properties to determine their universality classes through critical exponents and scaling functions.

Findings

Two main universality classes identified: abelian and stochastic models.

Non-abelian deterministic models show non-universal behavior.

Symmetry properties critically influence universality in sandpile models.

Abstract

The symmetry properties which determine the critical exponents and universality classes in conservative sandpile models are identified. This is done by introducing a set of models, including all possible combinations of abelian vs. non-abelian, deterministic vs. stochastic and isotropic vs. anisotropic toppling rules. The universality classes are determined by an extended set of critical exponents, scaling functions and geometrical features. Two universality classes are clearly identified: (a) the universality class of abelian models and (b) the universality class of stochastic models. In addition, it is found that non-abelian models with deterministic toppling rules exhibit non-universal behavior.