On Growth, Disorder, and Field Theory

Abstract

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.

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

References in corpus (3)

• Quantized Scaling of Growing Surfaces
• Non-perturbative renormalization of the KPZ growth dynamics
• Critical Discussion of the 2-Loop Calculations for the KPZ-Equation

Cited by in corpus (14)

• Quantum dynamical field theory for non-equilibrium phase transitions in driven open systems
• Phase Transitions and Scaling in Systems Far From Equilibrium
• When fast and slow interfaces grow together: connection to the half-space problem of the Kardar-Parisi-Zhang class
• Landau Theory for Non-Equilibrium Steady States
• Effects of junctional correlations in the totally asymmetric simple exclusion process on random regular networks
• The Kardar-Parisi-Zhang model of a random kinetic growth: effects of a randomly moving medium
• Non-Analytic Non-Equilibrium Field Theory: Stochastic Reheating of the Ising Model
• Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier-Stokes equation
• Effects of a local defect on one-dimensional nonlinear surface growth
• Energy landscapes in random systems, driven interfaces and wetting
• Efimov effect at the Kardar-Parisi-Zhang roughening transition
• Scaling approach to related disordered stochastic and free-fermion models
• Passive Tracer Dynamics in Slow-Bond Problem
• Local d'Alembertian for causal sets