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Low-temperature interfaces: prewetting, layering, faceting and Ferrari-Spohn diffusions. (English) Zbl 1414.60079
Summary: n this paper, we survey and discuss various surface phenomena such as prewetting, layering and faceting for a family of two- and three-dimensional low-temperature models of statistical mechanics, notably Ising models and \(2+1\)-dimensional solid-on-solid (SOS) models, with a particular accent on scaling regimes which lead or, in most cases, are conjectured to lead to Ferrari-Spohn type diffusions.

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
60F17 Functional limit theorems; invariance principles
60G60 Random fields