Crossover from rotational to stochastic sandpile universality in the random rotational sandpile model

TL;DR

This paper investigates a random rotational sandpile model to understand the crossover from rotational to Manna universality class, revealing a continuous dependence on toppling rule distribution and confirming the Manna class's existence.

Contribution

The study introduces a random rotational sandpile model and demonstrates a continuous crossover to the Manna universality class based on rule distribution.

Findings

Critical behavior depends on the proportion of toppling rules.

Equal proportions reproduce Manna model behavior.

Supports the existence of the Manna universality class.

Abstract

In the rotational sandpile model, either the clockwise or the anti-clockwise toppling rule is assigned to all the lattice sites. It has all the features of a stochastic sandpile model but belongs to a different universality class than the Manna class. A crossover from rotational to Manna universality class is studied by constructing a random rotational sandpile model and assigning randomly clockwise and anti-clockwise rotational toppling rules to the lattice sites. The steady state and the respective critical behaviour of the present model are found to have a strong and continuous dependence on the fraction of the lattice sites having the anti-clockwise (or clockwise) rotational toppling rule. As the anti-clockwise and clockwise toppling rules exist in equal proportions, it is found that the model reproduces critical behaviour of the Manna model. It is then further evidence of the existence of the Manna class, in contradiction with some recent observations of the non-existence of the Manna class.