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In this paper, we survey and discuss various surface phenomena such asprewetting, layering and faceting for a family of two- and three-dimensionallow-temperature models of statistical mechanics, notably Ising models and(2+1)-dimensional solid-on-solid (SOS) models, with a particular accent onscaling regimes which lead or, in most cases, are conjectured to lead toFerrari-Spohn type diffusions.

Low-temperature interfaces: Prewetting, layering, faceting and Ferrari-Spohn diffusions