Low-Temperature Interfaces: Prewetting, Layering, Faceting and Ferrari-Spohn Diffusions

D. Ioffe, Y. Velenik

2018, v.24, №3, 487-537

ABSTRACT

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.

Keywords: Lattice models of phase segregation, random interfaces, level lines, pre-wetting, layering, faceting, polymers with area tilts, effective random walks, ground states, Doob transform, Dyson\tire Ferrari-Spohn diffusions

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