DISTRIBUTION OF TERRACE WIDTHS ON A VICINAL SURFACE WITHIN THE ONE-DIMENSIONAL FREE-FERMION MODEL

For the terrace-step-kink model of a stepped surface, the distribution P (L) of terrace widths L is calculated at low temperature by mapping the problem onto the one-dimensional free-fermion model. In this approximation, the only energetic interaction between steps is a hard-core repulsion. A skewed distribution with a parabolic rise and a Gaussian tail is found; the exact asymptotic forms are displayed. By plotting [L] P(L) vs L/[L], we obtain a "universal" curve nearly independent of the average terrace width [L]. With use of this scaling property, analytic approximants are constructed and the role of correlations discussed. We present some results for steps with energetic interactions in two special cases.