Finite-size effects in roughness distribution scaling

Abstract

We study numerically finite-size corrections in scaling relations for roughness distributions of various interface growth models. The most common relation, which considers the average roughness $<w_2>$ as scaling factor, is not obeyed in the steady states of a group of ballistic-like models in 2+1 dimensions, even when very large system sizes are considered. On the other hand, good collapse of the same data is obtained with a scaling relation that involves the root mean square fluctuation of the roughness, which can be explained by finite-size effects on second moments of the scaling functions. We also obtain data collapse with an alternative scaling relation that accounts for the effect of the intrinsic width, which is a constant correction term previously proposed for the scaling of $<w_2>$. This illustrates how finite-size corrections can be obtained from roughness distributions scaling. However, we discard the usual interpretation that the intrinsic width is a consequence of high surface steps by analyzing data of restricted solid-on-solid models with various maximal height differences between neighboring columns. We also observe that large finite-size corrections in the roughness distributions are usually accompanied by huge corrections in height distributions and average local slopes, as well as in estimates of scaling exponents. The molecular-beam epitaxy model of Das Sarma and Tamborenea in 1+1 dimensions is a case example in which none of the proposed scaling relations works properly, while the other measured quantities do not converge to the expected asymptotic values. Thus, although roughness distributions are clearly better than other quantities to determine the universality class of a growing system, it is not the final solution for this task.

25 pages, including 9 figures and 1 table

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Cited by in corpus (15)

• Numerical study of the Kardar-Parisi-Zhang equation
• Universal fluctuations in radial growth models belonging to the KPZ universality class
• Universality and dependence on initial conditions in the class of the nonlinear molecular beam epitaxy equation
• Roughness exponents and grain shapes
• Scaling in reversible submonolayer deposition
• On the origins of scaling corrections in ballistic growth models
• Scaling of island size and capture zone distributions in submonolayer growth
• Crossover in the scaling of island size and capture zone distributions
• Scaling, cumulant ratios and height distribution of the ballistic deposition in 3+1 and 4+1 dimensions
• Scaling of local roughness distributions
• Width and extremal height distributions of fluctuating interfaces with window boundary conditions
• Growth instability due to lattice-induced topological currents in limited mobility epitaxial growth models
• Quasi-stationary states in nonlocal stochastic growth models with infinitely many absorbing states
• Height distributions in interface growth: The role of the averaging process
• Dimensional crossover in surface growth on rectangular substrates