Universal macroscopic background formation in surface super-roughening

We study a class of super-rough growth models whose structure factor satisfies the Family-Vicsek scaling. We demonstrate that a macroscopic background spontaneously develops in the local surface profile, which dominates the scaling of the local surface width and the height-difference. The shape of the macroscopic background takes a form of a finite-order polynomial whose order is decided from the value of the global roughness exponent. Once the macroscopic background is subtracted, the width of the resulting local surface profile satisfies the Family-Vicsek scaling. We show that this feature is universal to all super-rough growth models, and we also discuss the difference between the macroscopic background formation and the pattern formation in other models.Comment: 5 pages, LaTex, 1 figure, minor correction

Universality in two-dimensional Kardar-Parisi-Zhang growth

We analyze simulations results of a model proposed for etching of a crystalline solid and results of other discrete models in the 2+1-dimensional Kardar-Parisi-Zhang (KPZ) class. In the steady states, the moments W_n of orders n=2,3,4 of the heights distribution are estimated. Results for the etching model, the ballistic deposition (BD) model and the temperature-dependent body-centered restricted solid-on-solid model (BCSOS) suggest the universality of the absolute value of the skewness S = W_3 / (W_2)^(3/2) and of the value of the kurtosis Q = W_4 / (W_2)^2 - 3. The sign of the skewness is the same of the parameter \lambda of the KPZ equation which represents the process in the continuum limit. The best numerical estimates, obtained from the etching model, are |S| = 0.26 +- 0.01 and Q = 0.134 +- 0.015. For this model, the roughness exponent \alpha = 0.383 +- 0.008 is obtained, accounting for a constant correction term (intrinsic width) in the scaling of the squared interface width. This value is slightly below previous estimates of extensive simulations and rules out the proposal of the exact value \alpha=2/5. The conclusion is supported by results for the ballistic deposition model. Independent estimates of the dynamical exponent and of the growth exponent are 1.605 <= z <= 1.64 and \beta = 0.229 +- 0.005, respectively, which are consistent with the relations \alpha + z = 2 and z = \alpha / \beta.Comment: 8 pages, 9 figures, to be published in Phys. Rev.

Effect of Long-Range Interactions in the Conserved Kardar-Parisi-Zhang Equation

The conserved Kardar-Parisi-Zhang equation in the presence of long-range nonlinear interactions is studied by the dynamic renormalization group method. The long-range effect produces new fixed points with continuously varying exponents and gives distinct phase transitions, depending on both the long-range interaction strength and the substrate dimension $d$. The long-range interaction makes the surface width less rough than that of the short-range interaction. In particular, the surface becomes a smooth one with a negative roughness exponent at the physical dimension d=2.Comment: 4 pages(LaTex), 1 figure(Postscript

Scaling Approach to Calculate Critical Exponents in Anomalous Surface Roughening

We study surface growth models exhibiting anomalous scaling of the local surface fluctuations. An analytical approach to determine the local scaling exponents of continuum growth models is proposed. The method allows to predict when a particular growth model will have anomalous properties ($\alpha \neq \alpha_{loc}$) and to calculate the local exponents. Several continuum growth equations are examined as examples.Comment: RevTeX, 4 pages, no figs. To appear in Phys. Rev. Let

Reconstructed Rough Growing Interfaces; Ridgeline Trapping of Domain Walls

We investigate whether surface reconstruction order exists in stationary growing states, at all length scales or only below a crossover length, $l_{\rm rec}$. The later would be similar to surface roughness in growing crystal surfaces; below the equilibrium roughening temperature they evolve in a layer-by-layer mode within a crossover length scale $l_{\rm R}$, but are always rough at large length scales. We investigate this issue in the context of KPZ type dynamics and a checker board type reconstruction, using the restricted solid-on-solid model with negative mono-atomic step energies. This is a topology where surface reconstruction order is compatible with surface roughness and where a so-called reconstructed rough phase exists in equilibrium. We find that during growth, reconstruction order is absent in the thermodynamic limit, but exists below a crossover length $l_{\rm rec}>l_{\rm R}$, and that this local order fluctuates critically. Domain walls become trapped at the ridge lines of the rough surface, and thus the reconstruction order fluctuations are slaved to the KPZ dynamics

Non-universal exponents in interface growth

We report on an extensive numerical investigation of the Kardar-Parisi-Zhang equation describing non-equilibrium interfaces. Attention is paid to the dependence of the growth exponents on the details of the distribution of the noise. All distributions considered are delta-correlated in space and time, and have finite cumulants. We find that the exponents become progressively more sensitive to details of the distribution with increasing dimensionality. We discuss the implications of these results for the universality hypothesis.Comment: 12 pages, 5 figures; to appear in Phys. Rev. Let

Kinetic Roughening in Surfaces of Crystals Growing on Disordered Substrates

Substrate disorder effects on the scaling properties of growing crystalline surfaces in solidification or epitaxial deposition processes are investigated. Within the harmonic approach there is a phase transition into a low-temperature (low-noise) superrough phase with a continuously varying dynamic exponent z>2 and a non-linear response. In the presence of the KPZ nonlinearity the disorder causes the lattice efects to decay on large scales with an intermediate crossover behavior. The mobility of the rough surface hes a complex dependence on the temperature and the other physical parameters.Comment: 13 pages, 2 figures (not included). Submitted to Phys. Rev. Letts. Use Latex twic

Pattern Formation in Interface Depinning and Other Models: Erratically Moving Spatial Structures

We study erratically moving spatial structures that are found in a driven interface in a random medium at the depinning threshold. We introduce a bond-disordered variant of the Sneppen model and study the effect of extremal dynamics on the morphology of the interface. We find evidence for the formation of a structure which moves along with the growth site. The time average of the structure, which is defined with respect to the active spot of growth, defines an activity-centered pattern. Extensive Monte Carlo simulations show that the pattern has a tail which decays slowly, as a power law. To understand this sort of pattern formation, we write down an approximate integral equation involving the local interface dynamics and long-ranged jumps of the growth spot. We clarify the nature of the approximation by considering a model for which the integral equation is exactly derivable from an extended master equation. Improvements to the equation are considered by adding a second coupled equation which provides a self-consistent description. The pattern, which defines a one-point correlation function, is shown to have a strong effect on ordinary space-fixed two-point correlation functions. Finally we present evidence that this sort of pattern formation is not confined to the interface problem, but is generic to situations in which the activity at succesive time steps is correlated, as for instance in several other extremal models. We present numerical results for activity-centered patterns in the Bak-Sneppen model of evolution and the Zaitsev model of low-temperature creep.Comment: RevTeX, 18 pages, 19 eps-figures, To appear in Phys. Rev.

Dynamics of Particles Deposition on a Disordered Substrate: II. Far-from Equilibrium Behavior. -

The deposition dynamics of particles (or the growth of a rigid crystal) on a disordered substrate at a finite deposition rate is explored. We begin with an equation of motion which includes, in addition to the disorder, the periodic potential due to the discrete size of the particles (or to the lattice structure of the crystal) as well as the term introduced by Kardar, Parisi, and Zhang (KPZ) to account for the lateral growth at a finite growth rate. A generating functional for the correlation and response functions of this process is derived using the approach of Martin, Sigga, and Rose. A consistent renormalized perturbation expansion to first order in the non-Gaussian couplings requires the calculation of diagrams up to three loops. To this order we show, for the first time for this class of models which violates the the fluctuation-dissipation theorem, that the theory is renormalizable. We find that the effects of the periodic potential and the disorder decay on very large scales and asymptotically the KPZ term dominates the behavior. However, strong non-trivial crossover effects are found for large intermediate scales.Comment: 52 pages & 17 Figs in uucompressed file. UR-CM 94-090

Dynamic Scaling of Ion-Sputtered Surfaces

We derive a stochastic nonlinear equation to describe the evolution and scaling properties of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters characterizing the sputtering process. We find that transitions may take place between various scaling behaviors when experimental parameters such as the angle of incidence of the incoming ions or their average penetration depth, are varied.Comment: 13 pages, Revtex, 2 figure