Numerical study of the Langevin theory for Fixed Energy Sandpiles

José J. Ramasco1, Miguel A. Muñoz2 and Constantino A. da Silva Santos1
1Centro de Física do Porto and Departamento de Física, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal.
2Instituto de Física Téorica y Computacional Carlos I, Universidad de Granada, Facultad de Ciencias, 18071 Granada, Spain.

( July 2003)

The recently proposed Langevin equation, aimed to capture the relevant critical features of stochastic sandpiles, and other self-organizing systems is studied numerically. The 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 dierent 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.