ON GROWTH, DISORDER, AND FIELD-THEORY

This article reviews recent developments in statistical field theory f ar 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 i n a medium with quenched disorder. At strong stochastic driving-or at strong disorder, respectively-these systems develop non-perturbative s cale invariance. Presumably exact values of the scaling exponents foll ow from a self-consistent asymptotic theory. This theory is based on t he concept of an operator product expansion formed by the local scalin g fields. The key difference from standard Lagrangian field theory is the appearance of a dangerous irrelevant coupling constant generating dynamical anomalies in the continuum limit.