Vicinal surfaces and the Calogero-Sutherland model

A miscut (vicinal) crystal surface can be regarded as an array of meandering but noncrossing steps, Interactions between the steps are shown to induce a faceting transition of the rough surface between a homogeneous Tomonaga-Luttinger Liquid state and a low-temperature regime of local step clusters in coexistence with ideal facets. This morphological transition is governed by a hitherto neglected critical Line of the well-known Calogero-Sutherland model. Its exact solution yields expressions for measurable quantities that compare favorably with recent experiments on Si surfaces.