Field theory of long time behaviour in driven diffusive systems

H. K. Janssen, B. Schmittmann

Kwan-tai Leung, John Cardy

V. Becker, H. K. Janssen

Pierre Meystre, Edmond Geneux, A. Quattropani +1 more

V. Becker, H. K. Janssen

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 dc we find the critical scaling behaviour of the vertex functions in spatial dimensions d < dc. Its deviation from purely diffusive behaviour is characterized by the anomaly–exponent η that we calculate at first and second order, respectively in ǫ = dc − d. In each model η turns out to be positive which means superdiffusive spread of density fluctuations in the driving force direction. 1 1

Juha Honkonen, Antti J. Kupiainen

The authors present a field theoretic renormalisation group analysis of the critical behaviour of a diffusive system subject to an external field for the case of an odd induced current. The fixed-point equations are shown to impose constraints on the critical exponents. Below D c =3, the solution that is stable at one-loop order corresponds to a fixed point with anomalous dimensions vanishing to all orders.