Universality classes of the Kardar-Parisi-Zhang equation

Abstract

We re-examine mode-coupling theory for the Kardar-Parisi-Zhang (KPZ) equation in the strong coupling limit and show that there exists two branches of solutions. One branch (or universality class) only exists for dimensionalities $d<d_c=2$ and is similar to that found by a variety of analytic approaches, including replica symmetry breaking and Flory-Imry-Ma arguments. The second branch exists up to $d_c=4$ and gives values for the dynamical exponent $z$ similar to those of numerical studies for $d\ge 2$.

arXiv comment4 pages, 1 figure, published version

References in corpus (18)

• Exact scaling functions for one-dimensional stationary KPZ growth
• Critical Exponents of the KPZ Equation via Multi-Surface Coding Numerical Simulations
• Scaling Exponents for Kinetic Roughening in Higher Dimensions
• Width Distributions and the Upper Critical Dimension of KPZ Interfaces
• Upper critical dimension, dynamic exponent and scaling functions in the mode-coupling theory for the Kardar-Parisi-Zhang equation
• On the Perturbation Expansion of the KPZ-Equation
• Mode coupling and renormalization group results for the noisy Burgers equation
• Non-perturbative renormalization of the KPZ growth dynamics
• Glassy Solutions of the Kardar-Pasrisi-Zhang Equation
• The Nonequilibrium Dynamics of Driven Line Liquids
• Localized growth modes, dynamic textures, and upper critical dimension for the Kardar-Parisi-Zhang equation in the weak noise limit
• Stretched exponential relaxation in the mode-coupling theory for the Kardar-Parisi-Zhang equation
• 2-loop Functional Renormalization for elastic manifolds pinned by disorder in N dimensions
• Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem
• Numerical Solution of the Mode-Coupling Equations for the Kardar-Parisi-Zhang Equation in One Dimension
• Scale Invariant Dynamics of Surface Growth
• Directed polymers in a random medium: a variational approach
• Directed polymers and interfaces in random media : free-energy optimization via confinement in a wandering tube

Cited by in corpus (9)

• Numerical study of the Kardar-Parisi-Zhang equation
• Spatiotemporal structure of Lyapunov vectors in chaotic coupled-map lattices
• Mapping of 2+1-dimensional Kardar-Parisi-Zhang growth onto a driven lattice gas model of dimer
• Slow relaxation and aging kinetics for the driven lattice gas
• Finite scale singularity in the renormalization group flow of a reaction-diffusion system
• Scaling and universality in coupled driven diffusive models
• Universality class of replica symmetry breaking, scaling behavior, and the low-temperature fixed-point order function of the Sherrington-Kirkpatrick model
• Rough or crumpled: Strong coupling phases of a generalized Kardar-Parisi-Zhang surface
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles