Langevin theory of absorbing phase transitions with a conserved magnitude

TL;DR

This paper numerically investigates a Langevin equation coupled to a conserved field, supporting its role in describing a new universality class of absorbing phase transitions observed in sandpile models and related systems.

Contribution

It provides numerical evidence that the Langevin equation with a conserved field accurately captures the critical behavior of various models in this universality class.

Findings

Results match discrete models in 1, 2, and 3 dimensions.

Supports the Langevin equation as a valid theoretical framework.

Confirms the existence of a new universality class for absorbing phase transitions.

Abstract

The recently proposed Langevin equation, aimed to capture the relevant critical features of stochastic sandpiles, and other self-organizing systems is studied numerically. This equation is similar to the Reggeon field theory, describing generic systems with absorbing states, but it is coupled linearly to a second conserved and static (non-diffusive) field. It has been claimed to represent a new universality class, including different discrete models: the Manna as well as other sandpiles, reaction-diffusion systems, etc. In order to integrate the equation, and surpass the difficulties associated with its singular noise, we follow a numerical technique introduced by Dickman. Our results coincide remarkably well with those of discrete models claimed to belong to this universality class, in one, two, and three dimensions. This provides a strong backing for the Langevin theory of stochastic sandpiles, and to the very existence of this new, yet meagerly understood, universality class.