Abstract

Low-temperature interfaces: Prewetting, layering, faceting and Ferrari-Spohn diffusions D. Ioffe, Y. Velenik Markov Process. Related Fields 24, 487-537 (2016). In 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. Key words: Invariance principle, critical prewetting, entropic repulsion, ordered random walks, non-crossing random walks, non-intersecting random walks, Ferrari-Spohn diffusions, Ising model, Blume-Capel model, wetting, prewetting, faceting, SOS model Files: PDF file, Published version, bibtex