NUMERICAL-ANALYSIS OF A LANGEVIN EQUATION FOR SYSTEMS WITH INFINITE ABSORBING STATES

One-dimensional systems with an infinite number of absorbing states ex hibit a phase transition that is not fully understood yet. Their stati c critical exponents are universal and belong in the Reggeon field the ory (or directed percolation) universality class. However, exponents a ssociated with the spreading of a localized seed appear to be nonunive rsal depending on the nature of the initial condition. We investigate this problem by integrating numerically a non-Markovian Langevin equat ion proposed recently to describe such phase transitions. We find that the static critical exponents are universal, as expected. On the othe r hand, the Langevin equation reproduces the nonuniversal behavior obs erved in microscopic models for exponents associated with the spreadin g of an initially localized seed and satisfies the generalized hypersc aling relation proposed for those systems.