Finite-size effects in roughness distribution scaling.

Area of Science:

• Surface science
• Statistical physics
• Computational physics

Background:

• Interface growth models are fundamental in understanding surface evolution.
• Scaling relations are used to describe universal behavior in these systems.
• Finite-size effects can significantly alter observed scaling behavior.

Purpose of the Study:

• To investigate finite-size corrections in scaling relations for interface growth models.
• To evaluate the effectiveness of different scaling approaches for roughness distributions.
• To understand the origin of intrinsic width and its impact on scaling.

Main Methods:

• Numerical simulations of various interface growth models.
• Analysis of roughness distributions and scaling relations.
• Investigation of restricted solid-on-solid models with varying height differences.

Main Results:

• The common scaling relation using average roughness fails for some ballisticlike models.
• Scaling relations involving root mean square roughness fluctuations and intrinsic width show good data collapse.
• Finite-size corrections in roughness distributions correlate with corrections in height and slope distributions.

Conclusions:

• Root mean square roughness and intrinsic width provide better scaling descriptions than average roughness.
• The intrinsic width is not solely due to high surface steps.
• While roughness distributions are valuable for determining universality classes, they are not a definitive solution.