Existence of the upper critical dimension of the Kardar-Parisi-Zhang equation
arXiv:cond-mat/0012103 · doi:10.1016/S0378-4371(02)00553-8
Abstract
The controversy whether or not he Kardar-Parisi-Zhang (KPZ) equation has an upper critical dimension (UCD) is going on for quite a long time. Some approximate integral equations for the two-point function served as an indication for the existence of a UCD, by obtaining a dimension, above which the equation does not have a strong coupling solution. A surprising aspect of these studies, however, is that variuos authors that considered the same equation produced large variations in the UCD. This caused some doubts concerning the existence of a UCD. Here we revisit these calculations, describe the reason for such large variations in the results of identical calculations, show by a large-d expansion that indeed there exist a UCD and then obtain it numerically by properly defining the integrals involved.
18 pages
References in corpus (2)
Cited by in corpus (23)
- Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation
- Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications
- Upper critical dimension of the KPZ equation
- Multi-surface coding simulations of the restricted solid-on-solid model in four dimensions
- Growing Surfaces with Anomalous Diffusion - Results for the Fractal Kardar-Parisi-Zhang Equation
- Growth exponents of the etching model in high dimensions
- The ideas behind the Self Consistent Expansion
- Dynamical Inequality in Growth Models
- Static approach to renormalization group analysis of stochastic models with spatially quenched disorder
- Patterns in the Kardar-Parisi-Zhang equation
- Numerical integration of KPZ equation with restrictions
- Growth models on the Bethe lattice
- 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
- Thermally driven elastic membranes are quasi-linear across all scales
- The Structure of Fluctuating Thin Sheets Under Random Forcing
- Dynamics of Fluctuating Thin Sheets Under Random Forcing
- Nonlinear field theories during homogeneous spatial dilation
- Localization transition of stiff directed lines in random media
- Asymptotic Matching the Self-Consistent Expansion to Approximate the Modified Bessel Functions of the Second Kind
- Random Walk on a Random Surface: Implications of Non-perturbative Concepts and Dynamical Emergence of Galilean Symmetry
- Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles