Field Theory of Critical Behavior in Driven Diffusive Systems with Quenched Disorder

We present a field-theoretic renormalization-group study for the critical behavior of a uniformly driven diffusive system with quenched disorder, which is modeled by different kinds of potential barriers between sites. Due to their symmetry properties, these different realizations of the random potential barriers lead to three different models for the phase transition to transverse order and to one model for the phase transition to longitudinal order all belonging to distinct universality classes. In these four models, which have different upper critical dimensions d_c, we find the critical scaling behavior of the vertex functions in spatial dimensions d<d_c. The deviation from purely diffusive behavior is characterized by the anomaly exponent , which we calculate at first and second order, respectively, in =d_c–d. In each model turns out to be positive, which means superdiffusive spread of density fluctuations in the driving force direction.