We characterize the crossover regime to the KPZ equation for a class of one-dimensional weakly asymmetric exclusion processes. The crossover depends on the strength asymmetry an 2-γ (a, γ > 0) and it occurs at γ = 1/2. We show that the density field is a solution of an Ornstein-Uhlenbeck equation if g Î (1/2,1]{gammain(1/2,1]} , while for γ = 1/2 it is an energy solution of the KPZ equation. The corresponding crossover for the current of particles is readily obtained.
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