Interacting Steps With Finite-Range Interactions: Analytical Approximation and Numerical Results

Abstract

We calculate an analytical expression for the terrace-width distribution $P(s)$ for an interacting step system with nearest and next nearest neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent 1D system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions $q$ on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

9 pages, 9 figures

References in corpus (4)

• Using the Wigner-Ibach Surmise to Analyze Terrace-Width Distributions: History, User's Guide, and Advances
• Equilibrium distributions in thermodynamical traffic gas
• Relaxation of Terrace-width Distributions: Physical Information from Fokker-Planck Time
• Mean-Field Approximation for Spacing Distribution Functions in Classical Systems

Cited by in corpus (1)

• The inverse-square interaction phase diagram: unitarity in the bosonic ground state