Directed Fixed Energy Sandpile Model

TL;DR

This paper investigates a directed fixed energy sandpile model, revealing a continuous phase transition at a critical density with distinct exponents for deterministic and stochastic versions, enhancing understanding of self-organized criticality.

Contribution

It introduces a directed fixed energy sandpile model and compares deterministic and stochastic dynamics, highlighting differences in critical behavior and exponents.

Findings

Continuous phase transition at critical density

Deterministic model exhibits nontrivial exponents

Stochastic model shows mean field like exponents

Abstract

We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around a critical density. While the deterministic version has the set of nontrivial exponents, the stochastic model is characterized by mean field like exponents.