Langevin theory of absorbing phase transitions with a conserved magnitude

• Published in: arXiv.org
• Main Authors: Ramasco, J J, Munoz, M A, C A da Silva Santos
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 16.07.2003
• Subjects: Field theory; Mathematical models; Phase transitions; Self organizing systems
• DOI: 10.48550/arxiv.0307406

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.