Numerical study of the Langevin theory for fixed-energy sandpiles.
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 (nondiffusive) field. It has been claimed to represent a different 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 meagerly understood universality class.
Ramasco
José J
JJ
Departamento de Física and Centro de Física do Porto, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal.
Muñoz
Miguel A
MA
da Silva Santos
Constantino A
CA