Langevin theory of absorbing phase transitions with a conserved magnitude

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.

4 pages, 3 eps figs, submitted to PRL

References in corpus (3)

• Universality class of nonequilibrium phase transitions with infinitely many-absorbing-states
• Universal scaling behavior at the upper critical dimension of non-equilibrium continuous phase transitions
• Scaling behavior of the conserved transfer threshold process

Cited by in corpus (13)

• Integration of Langevin Equations with Multiplicative Noise and Viability of Field Theories for Absorbing Phase Transitions
• Activated Random Walkers: Facts, Conjectures and Challenges
• The Oslo model, hyperuniformity, and the quenched Edwards-Wilkinson model
• A simple sandpile model of active-absorbing state transitions
• Dynamic correlations in the conserved Manna sandpile
• Sticky grains do not change the universality class of isotropic sandpiles
• Diffusion in stochastic sandpiles
• Hydrodynamics, density fluctuations and universality in conserved stochastic sandpiles
• Activity, diffusion, and correlations in a two-dimensional conserved stochastic sandpile
• Absorbing-state phase transitions: exact solutions of small systems
• Equivalence of operator-splitting schemes for the integration of the Langevin equation
• Conserved sandpile with a variable height restriction
• Critical Density of the Abelian Manna Model via a Multi-type Branching Process