Finite-size effects in roughness distribution scaling

Details Finite-size effects in roughness distribution scaling Finite-size effects in roughness distribution scaling

2007-06-11

arxiv.org/abs/0706.1307v2

Phys. Rev. E 76, 061601 (2007)

Physics

Condensed Matter

Statistical Mechanics

25 pages, including 9 figures and 1 table

Scientific paper

10.1103/PhysRevE.76.061601

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 $$ as scaling factor, is not obeyed in the steady states of a group of ballistic-like models in 2+1 dimensions, even when very large system sizes are considered. On the other hand, good collapse of the same data is obtained with a scaling relation that involves the root mean square fluctuation of the roughness, which can be explained by finite-size effects on second moments of the scaling functions. We also obtain data collapse with an alternative scaling relation that accounts for the effect of the intrinsic width, which is a constant correction term previously proposed for the scaling of $$. 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.

Affiliated with

Also associated with

No associations

Rating

Finite-size effects in roughness distribution scaling does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Finite-size effects in roughness distribution scaling, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite-size effects in roughness distribution scaling will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-178829