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

TL;DR

This paper uses field theory and renormalization group methods to analyze the critical behavior of driven diffusive systems with quenched disorder, revealing distinct universality classes and superdiffusive fluctuation spreading.

Contribution

It introduces a field theoretic approach to classify phase transitions in driven disordered systems into different universality classes based on symmetry properties.

Findings

Identifies three models for transverse order and one for longitudinal order with distinct universality classes.

Calculates the anomaly-exponent ta at first and second order, showing superdiffusive behavior.

Determines the critical scaling behavior of vertex functions below the upper critical dimension.

Abstract

We present a field theoretic renormalization group study for the critical behaviour of a uniformly driven diffusive system with quenched disorder, which is modelled 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 that have different upper critical dimensions d_{c} we find the critical scaling behaviour of the vertex functions in spatial dimensions d < d_{c} . Its deviation from purely diffusive behaviour is characterized by the anomaly-exponent \eta that we calculate at first and second order, respectively in $\epsilon = d_{c} -d$. In each model \eta turns out to be positive which means superdiffusive spread of density fluctuations in the driving force direction.