The roughening transition of crystal surfaces. I. static and dynamic renormalization theory, crystal shape and facet growth

Abstract

The renormalization approach to the roughening transition is reconsidered, both in a static and in a dynamic picture. Earlier results based on an asymptotic approximation are corrected, especially as regards the interface mobility. For a tilted interface, or in the presence of an applied force F, a new length scale appears, which must be compared to the correlation length ξ. As a result, the roughening transition is blurred, the crossover occurring below TR. This crossover is approached from both ends, via a « stopped renormalization » technique on the rough side, within a « discrete step » picture in the faceted state. At this last stage, the discussion is mostly qualitative. Comparison with experiment is done elsewhere.