Scaling Exponents for Kinetic Roughening in Higher Dimensions

Abstract

We discuss the results of extensive numerical simulations in order to estimate the scaling exponents associated with kinetic roughening in higher dimensions, up to d=7+1. To this end, we study the restricted solid - on - solid growth model, for which we employ a novel fitting {\it ansatz} for the spatially averaged height correlation function $\bar{G}(t)\sim t^{2\beta }$ to estimate the scaling exponent $\beta$. Using this method, we present a quantitative determination of $\beta$ in d=3+1 and 4+1 dimensions. To check the consistency of these results, we also compute the interface width and determine $\beta$ and $\chi$ from it independently. Our results are in disagreement with all existing theories and conjectures, but in four dimensions they are in good agreement with recent simulations of Forrest and Tang [{\it Phys. Rev. Lett.} {\bf 64}:1405 (1990)] for a different growth model. Above five dimensions, we use the time dependence of the width to obtain lower bound estimates for $\beta$. Within the accuracy of our data, we find no indication of an upper critical dimension up to d=7+1.

17 pages, TEX, figures upon request from [email protected]

References in corpus (1)

• The Nonequilibrium Dynamics of Driven Line Liquids

Cited by in corpus (66)

• Universality classes in nonequilibrium lattice systems
• Keldysh Field Theory for Driven Open Quantum Systems
• Dynamic Scaling of Ion-Sputtered Surfaces
• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation
• Critical Exponents of the KPZ Equation via Multi-Surface Coding Numerical Simulations
• 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
• Nonlinear Measures for Characterizing Rough Surface Morphologies
• On the Renormalization of the Kardar-Parisi-Zhang equation
• Mode coupling and renormalization group results for the noisy Burgers equation
• Universality in two-dimensional Kardar-Parisi-Zhang growth
• Quantized Scaling of Growing Surfaces
• Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1 and 3+1 dimensions
• Non-perturbative renormalization of the KPZ growth dynamics
• Glassy Solutions of the Kardar-Pasrisi-Zhang Equation
• Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension
• Electrodynamic duality and vortex unbinding in driven-dissipative condensates
• Soliton approach to the noisy Burgers equation: Steepest descent method
• Stretched exponential relaxation in the mode-coupling theory for the Kardar-Parisi-Zhang equation
• The Kardar-Parisi-Zhang equation with spatially correlated noise: a unified picture from nonperturbative renormalization group
• Directed d-mer diffusion describing Kardar-Parisi-Zhang type of surface growth
• Upper critical dimension of the KPZ equation
• Multi-surface coding simulations of the restricted solid-on-solid model in four dimensions
• High dimensional behavior of the Kardar-Parisi-Zhang growth dynamics
• Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem
• Mean-field limit of systems with multiplicative noise
• Non-universal exponents in interface growth
• Probing the tails of the ground state energy distribution for the directed polymer in a random medium of dimension $d=1,2,3$ via a Monte-Carlo procedure in the disorder
• Existence of the upper critical dimension of the Kardar-Parisi-Zhang equation
• Anomalous scaling at non-thermal fixed points of Burgers' and Gross-Pitaevskii turbulence
• Statistics of renormalized on-site energies and renormalized hoppings for Anderson localization models in dimensions d=2 and d=3
• On Growth, Disorder, and Field Theory
• Growth exponents of the etching model in high dimensions
• Scale Invariant Dynamics of Surface Growth
• Soluble Infinite-Range Model of Kinetic Roughening
• Random Transverse Field Ising Model in dimension $d>1$ : scaling analysis in the disordered phase from the Directed Polymer model
• Overlap, Disorder and Directed Polymers: A Renormalization Group Approach -
• Simulations of deposition growth models in various dimensions. Are overhangs important?
• Stochastic Model in the Kardar-Parisi-Zhang Universality With Minimal Finite Size Effects
• Faceted patterns and anomalous surface roughening driven by long-term correlated noise
• Universality classes of the Kardar-Parisi-Zhang equation
• 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
• Strong-coupling phases of the anisotropic Kardar-Parisi-Zhang equation
• Freezing transition of the directed polymer in a $1+d$ random medium : location of the critical temperature and unusual critical properties
• Scaling, cumulant ratios and height distribution of the ballistic deposition in 3+1 and 4+1 dimensions
• Statistics of low energy excitations for the directed polymer in a $1+d$ random medium ($d=1,2,3$)
• Matrix generalizations of some dynamic field theories
• Kardar-Parisi-Zhang universality class in ($d+1$)-dimensions
• Solid on Solid Model for Surface Growth in 2+1 Dimensions
• Improved Perturbation Theory for the Kardar-Parisi-Zhang Equation
• Growth diversity in one dimensional fluctuating interfaces
• Disorder-dominated phases of random systems : relations between tails exponents and scaling exponents
• Random Transverse Field Ising Model in dimension $d=2,3$ : Infinite Disorder scaling via a non-linear transfer approach
• Growth models on the Bethe lattice
• Numerical integration of KPZ equation with restrictions
• Kinetic roughening of the urban skyline
• Efimov effect at the Kardar-Parisi-Zhang roughening transition
• Surface growth on treelike lattices and the upper critical dimension of the KPZ class
• A numerical study of the development of bulk scale-free structures upon growth of self-affine aggregates
• Stiff directed lines in random media
• Random Walk on a Random Surface: Implications of Non-perturbative Concepts and Dynamical Emergence of Galilean Symmetry
• Directed polymers on a Cayley tree with spatially correlated disorder
• Invading interfaces and blocking surfaces in high dimensional disordered systems
• Renormalization group study of one-dimensional systems with roughening transitions