Characteristics of Deterministic and Stochastic Sandpile Models in a Rotational Sandpile Model

TL;DR

This paper introduces a new rotational sandpile model with a rotational constraint affecting sand flow, revealing critical exponents and behaviors that blend deterministic and stochastic features in self-organized criticality.

Contribution

A novel quasi-deterministic rotational sandpile model is developed, demonstrating unique critical exponents and scaling behaviors in non-equilibrium steady states.

Findings

Critical exponents characterize avalanche properties.

Probability distributions obey finite size scaling.

Model exhibits features of both deterministic and stochastic sandpiles.

Abstract

Rotational constraint representing a local external bias generally has non-trivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena. In order to study the effect of rotational bias in a out of equilibrium situation like self-organized criticality, a new two state ``quasi-deterministic'' rotational sandpile model is developed here imposing rotational constraint on the flow of sand grains. An extended set of new critical exponents are found to characterize the avalanche properties at the non-equilibrium steady state of the model. The probability distribution functions are found to obey usual finite size scaling supported by negative time autocorrelation between the toppling waves. The model exhibits characteristics of both deterministic and stochastic sandpile models.