I. INTRODUCTION

II. THREE PERSPECTIVES OF THE STANDARD MODEL

A. The microscopic driven lattice gas

B. Dynamic mean-field theories

C. A mesoscopic Langevin equation

III. LONG RANGE CORRELATIONS ABOVE CRITICALITY

A. Generic singularities in two-point functions

1. Power law and exponential decays
2. A fixed line of Gaussian dynamic models

B. Three-point correlation functions

IV. CRITICAL PHENOMENA

A. Simulation studies

1. Signals of a phase transition
2. Two-point correlations
   1. Anisotropic structure factors, the order parameter and the exponents
   2. Critical power law decays and the exponents
   3. Response functions and susceptibilities
   4. Internal energy and specific heat
3. Higher Correlations
   1. Three-point function
   2. Fluctuations in the structure factor and the internal energy
4. Finite size effects in the standard model

B. Theoretical investigations

1. General scaling laws with strong anisotropy
2. Field theoretic renormalisation group analysis
   1. The dynamic functional and the upper critical dimension
   2. Exponents and scaling functions in the tree approximation
   3. One-loop and exact results: the full scaling behavior
   4. Related models

V. PHYSICS BELOW CRITICALITY

A. The co-existence curve

B. Dynamics of phase separation

C. Interfacial properties in steady states

1. Suppression of interfacial rougheness
2. Shifted boundary conditions and `tilted' interfaces
   1. Dependence of bulk properties on interface orientation
   2. Domain splitting and merging
3. Numerical and theoretical studies

VI. VARIATIONS OF THE STANDARD MODEL

A. Random drive and multiple temperature models

1. Collective behavior above T
2. Phase transitions and critical properties of the bulk
3. Anomalous correlations of interfacial fluctuations
4. Combinations of direct and random drives

B. Chemical potential gradients and drive defects

1. Systems with a chemical potential gradient only
2. Finger formation in combined drives
3. Effects of line defects in external fields
4. Stability of an interface in a transverse chemical potential gradient

C. The two layer system

D. Multi-species models

1. The blocking transition
2. The polarized lattice gas

E. Repulsive interactions

F. Quenched random impurities

G. Special limits

1. Extreme anisotropic rates
2. Models in one dimension
   1. Systems with translational invariance
   2. Open boundary conditions, blockages and shocks
   3. Two-species models
   4. The Toom interface, a model with long range jumps

VII. RELATED NON-EQUILIBRIUM STEADY STATE SYSTEMS

A. Models with competing conserved and non-conserved dynamics

B. Multi-temperature models with Glauber dynamics

C. Models for driven interfaces

D. Gel electrophoresis and polymers in sedimentation

E. Self-organized criticality and other models of generic scale invariance

F. Liquids in non-equilibrium steady states

1. Linearized hydrodynamics far from criticality
2. Phase transitions under shear

VIII. SUMMARY AND OUTLOOK

 VT Physics     Royce Zia     Beate Schmittmann