Sticky grains do not change the universality class of isotropic sandpiles

TL;DR

This study demonstrates that isotropic sandpiles with sticky grains do not belong to the directed percolation universality class but instead share critical properties with the Manna class, due to conservation laws.

Contribution

It provides evidence that sticky grains do not alter the universality class of isotropic sandpiles, contrasting previous claims, and clarifies the role of conservation laws in critical behavior.

Findings

Isotropic sandpiles with sticky grains follow Manna class critical properties.

Simulations show deviation from directed percolation universality.

Langevin equations converge to Manna class dynamics upon coarse-graining.

Abstract

We revisit the sandpile model with ``sticky'' grains introduced by Mohanty and Dhar [Phys. Rev. Lett. {\bf 89}, 104303 (2002)] whose scaling properties were claimed to be in the universality class of directed percolation for both isotropic and directed models. Simulations in the so-called fixed-energy ensemble show that this conclusion is not valid for isotropic sandpiles and that this model shares the same critical properties of other stochastic sandpiles, such as the Manna model. %as expected from the existence of an extra %conservation-law, absent in directed percolation. These results are strengthened by the analysis of the Langevin equations proposed by the same authors to account for this problem which we show to converge, upon coarse-graining, to the well-established set of Langevin equations for the Manna class. Therefore, the presence of a conservation law keeps isotropic sandpiles, with or without stickiness, away from the directed percolation class.