Low-temperature interfaces: prewetting, layering, faceting and Ferrari-Spohn diffusions. (English) Zbl 1414.60079

Ioffe, D.; Velenik, Y.

Markov Process. Relat. Fields 24, No. 3, 487-537 (2018).

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.

MSC:

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

Keywords:

lattice models of phase segregation; random interfaces; level lines; prewtting; layering; faceting; polymers with area tilts; effective random walks; ground states; Doob transform; Dyson-Ferrari-Spohn diffusions