Numerical analysis of a Langevin equation for systems with infinite absorbing states

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Abstract
One-dimensional systems with an infinite number of absorbing states exhibit a phase transition that is not fully understood yet. Their static critical exponents are universal and belong in the Reggeon field theory (or directed percolation) universality class. However, exponents associated with the spreading of a localized seed appear to be nonuniversal depending on the nature of the initial condition. We investigate this problem by integrating numerically a non-Markovian Langevin equation proposed recently to describe such phase transitions. We find that the static critical exponents are universal, as expected. On the other hand, the Langevin equation reproduces the nonuniversal behavior observed in microscopic models for exponents associated with the spreading of an initially localized seed and satisfies the generalized hyperscaling relation proposed for those systems.