Interacting steps with finite-range interactions: Analytical approximation and numerical results

摘要

We calculate an analytical expression for the terrace-width distribution P(s) for an interacting step systemnwith nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto anstatistically equivalent one-dimensional system of classical particles. The validity of the model is tested withnseveral numerical simulations and experimental results. We explore the effect of the range of interactions q onnthe functional form of the terrace-width distribution and pair correlation functions. For physically plausibleninteractions, we find modest changes when next-nearest neighbor interactions are included and generallynnegligible changes when more distant interactions are allowed.We discuss methods for extracting from simulatednexperimental data the characteristic scale-setting terms in assumed potential forms.