On the Renormalization of the Kardar-Parisi-Zhang equation
arXiv:cond-mat/9501094 · doi:10.1016/0550-3213(95)00268-W
Abstract
The Kardar-Parisi-Zhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally subtracted perturbation expansion about d = 2. For the KPZ roughening transition in dimensions d > 2, this renormalization group yields the dynamic exponent z* = 2 and the roughness exponent chi* = 0, which are exact to all orders in epsilon = (2 - d)/2. The expansion becomes singular in d = 4, which is hence identified with the upper critical dimension of the KPZ equation. The implications of this perturbation theory for the strong-coupling phase are discussed. In particular, it is shown that the correlation functions and the coupling constant defined in minimal subtraction develop an essential singularity at the strong-coupling fixed point.
21 pp. (latex, now texable everywhere, no other changes), with 2 fig.
References in corpus (4)
Cited by in corpus (59)
- Universality classes in nonequilibrium lattice systems
- Critical Exponents of the KPZ Equation via Multi-Surface Coding Numerical Simulations
- Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
- Upper critical dimension, dynamic exponent and scaling functions in the mode-coupling theory for the Kardar-Parisi-Zhang equation
- Width Distributions and the Upper Critical Dimension of KPZ Interfaces
- Extremely large scale simulation of a Kardar-Parisi-Zhang model using graphics cards
- On the Perturbation Expansion of the KPZ-Equation
- Mode coupling and renormalization group results for the noisy Burgers equation
- Quantized Scaling of Growing Surfaces
- A pseudo-spectral method for the Kardar-Parisi-Zhang equation
- Canonical phase space approach to the noisy Burgers equation: Probability distributions
- Soliton approach to the noisy Burgers equation: Steepest descent method
- Phase Transitions and Scaling in Systems Far From Equilibrium
- The Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension
- Directed d-mer diffusion describing Kardar-Parisi-Zhang type of surface growth
- Functional renormalization group for anisotropic depinning and relation to branching processes
- Quantum spectrum as a time series : Fluctuation measures
- High dimensional behavior of the Kardar-Parisi-Zhang growth dynamics
- Multi-surface coding simulations of the restricted solid-on-solid model in four dimensions
- New Results for the Nonlocal Kardar-Parisi-Zhang Equation
- Critical Discussion of the 2-Loop Calculations for the KPZ-Equation
- Recent results on multiplicative noise
- Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem
- Cusps and shocks in the renormalized potential of glassy random manifolds: How Functional Renormalization Group and Replica Symmetry Breaking fit together
- Growing Surfaces with Anomalous Diffusion - Results for the Fractal Kardar-Parisi-Zhang Equation
- The Freezing of Random RNA
- Existence of the upper critical dimension of the Kardar-Parisi-Zhang equation
- Short-time scaling behavior of growing interfaces
- On Growth, Disorder, and Field Theory
- Growth exponents of the etching model in high dimensions
- Scale Invariant Dynamics of Surface Growth
- Derivation of the Functional Renormalization Group Beta-Function at order 1/N for Manifolds Pinned by Disorder
- Universality of (2+1)-dimensional restricted solid-on-solid models
- Universality classes in anisotropic non-equilibrium growth models
- Ageing of the 2+1 dimensional Kardar-Parisi-Zhang model
- Stochastic dynamics of chemotactic colonies with logistic growth
- Intermittency of Height Fluctuations and Velocity Increment of The Kardar-Parisi-Zhang and Burgers Equations with infinitesimal surface tension and Viscosity in 1+1 Dimensions
- Statistical Theory for the Kardar-Parisi-Zhang Equation in 1+1 Dimension
- Correlations, soliton modes, and non-Hermitian linear mode transmutation in the 1D noisy Burgers equation
- Scaling behavior in a stochastic self-gravitating system
- Universality class of replica symmetry breaking, scaling behavior, and the low-temperature fixed-point order function of the Sherrington-Kirkpatrick model
- Random interface growth in random environment: Renormalization group analysis of a simple model
- Directed polymers in high dimensions
- Marching on a rugged landscape: Universality in disordered asymmetric exclusion processes
- Scaling function for the noisy Burgers equation in the soliton approximation
- Canonical phase space approach to the noisy Burgers equation
- Field Theory of Disordered Elastic Interfaces at 3-Loop Order: Critical Exponents and Scaling Functions
- The Kardar-Parisi-Zhang model of a random kinetic growth: effects of a randomly moving medium
- Comparison of Different Parallel Implementations of the 2+1-Dimensional KPZ Model and the 3-Dimensional KMC Model
- Static approach to renormalization group analysis of stochastic models with spatially quenched disorder
- Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier-Stokes equation
- Stirred Kardar-Parisi-Zhang equation with quenched random noise: Emergence of induced nonlinearity
- Efimov effect at the Kardar-Parisi-Zhang roughening transition
- Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment
- Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
- Random Walk on a Random Surface: Implications of Non-perturbative Concepts and Dynamical Emergence of Galilean Symmetry
- Auxiliary Field Loop Expansion for the Effective Action for Stochastic Partial Differential Equations I
- Renormalization group study of one-dimensional systems with roughening transitions
- Interface roughening with nonlinear surface tension