Fixed-Energy Sandpiles Belong Generically to Directed Percolation

TL;DR

This study investigates fixed-energy sandpile models and finds that their critical behavior aligns with directed percolation, challenging the idea of a separate Manna universality class.

Contribution

The paper provides numerical evidence that fixed-energy sandpile models in the Manna class ultimately exhibit directed percolation behavior, questioning the existence of an independent universality class.

Findings

Critical behavior converges to directed percolation

Challenges the existence of a separate Manna universality class

Long-time simulations show universal behavior

Abstract

Fixed-energy sandpiles with stochastic update rules are known to exhibit a nonequilibrium phase transition from an active phase into infinitely many absorbing states. Examples include the conserved Manna model, the conserved lattice gas, and the conserved threshold transfer process. It is believed that the transitions in these models belong to an autonomous universality class of nonequilibrium phase transitions, the so-called Manna class. Contrarily, the present numerical study of selected (1+1)-dimensional models in this class suggests that their critical behavior converges to directed percolation after very long time, questioning the existence of an independent Manna class.