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Langevin theory of absorbing phase transitions with a conserved magnitude

J. J. Ramasco·M. A. Munoz·C. A. da Silva Santos
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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.

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J. J. Ramasco, M. A. Munoz, C. A. da Silva Santos. 2003-07-16. Langevin theory of absorbing phase transitions with a conserved magnitude. https://doi.org/10.1103/physreve.69.045105

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