Localization and delocalization of random interfaces. (English) Zbl 1189.82051

Velenik, Yvan

Probab. Surv. 3, 112-169 (2006).

Summary: The probabilistic study of effective interface models has been quite active in recent years, with a particular emphasis on the effect of various external potentials (wall, pinning potential, etc.) leading to localization/delocalization transitions. I review some of the results that have been obtained. In particular, I discuss pinning by a local potential, entropic repulsion and the (pre)wetting transition, both for models with continuous and discrete heights.

MSC:

82B41	Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
60K35	Interacting random processes; statistical mechanics type models; percolation theory
82B24	Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics
82B27	Critical phenomena in equilibrium statistical mechanics
82-02	Research exposition (monographs, survey articles) pertaining to statistical mechanics

Keywords:

random interfaces; random surfaces; roughening; entropic repulsion; pinning; wetting; prewetting