On Growth, Disorder, and Field Theory

Details On Growth, Disorder, and Field Theory On Growth, Disorder, and Field Theory

1998-06-26

arxiv.org/abs/cond-mat/9806330v2

J.Phys. C10 (1998) 9905

Physics

Condensed Matter

review article, 50 pages (latex), 10 figures (eps), minor modification of original version

Scientific paper

This article reviews recent developments in statistical field theory far from equilibrium. It focuses on the Kardar-Parisi-Zhang equation of stochastic surface growth and its mathematical relatives, namely the stochastic Burgers equation in fluid mechanics and directed polymers in a medium with quenched disorder. At strong stochastic driving -- or at strong disorder, respectively -- these systems develop nonperturbative scale-invariance. Presumably exact values of the scaling exponents follow from a self-consistent asymptotic theory. This theory is based on the concept of an operator product expansion formed by the local scaling fields. The key difference to standard Lagrangian field theory is the appearance of a dangerous irrelevant coupling constant generating dynamical anomalies in the continuum limit.

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