Entropic repulsion of an interface in an external field

Abstract

We consider an interface above an attractive hard wall in the complete wetting regime, and submitted to the action of an external increasing, convex potential, and study its delocalization as the intensity of this potential vanishes. Our main motivation is the analysis of critical prewetting, which corresponds to the choice of a linear external potential.We also present partial results on critical prewetting in the two dimensional Ising model, as well as a few (weak) results on pathwise estimates for the pure wetting problem for effective interface models.

An Invariance Principle to Ferrari–Spohn Diffusions

“…When c is above a critical threshold, the bulk of the system is occupied by a positively magnetized phase, while the walls are wet by a film of (unstable) negatively magnetized phase [16]. For a slightly different geometry, it was shown in [18] that this film has a width (along the walls) of order h −1/3+o (1) as h ↓ 0.…”

“…-Critical prewetting in the 2d Ising model: behavior of the film of unstable negatively magnetized layer induced by (−)-boundary conditions, in the presence of a positive bulk magnetic field [18]; see Figure 1. -Interfacial adsorption at the interface between two equilibrium phases [13,17].…”

Wetting of gradient fields: pathwise estimates

“…A common choice if V (x) = x 2 (usually termed a mass term), but given the situation we want to model here a more natural choice is V (x) = |x|. The latter choice allows for the interpretation of the interface as separating a thermodynamically stable phase (above) from a thermodynamically unstable phase (below), the latter being stabilized locally because it is favored by the wall; λ then measures the difference of free energies between the stable and unstable phases (both being stable when λ = 0); see [17,18] for a more detailed explanation. Finally, for η > 0, the measure…”

“…The situation studied in [14,17] is the following: Fix 0 ≤ η < η c , in dimension 1 or 2, or take η = 0 in dimension 3 and larger. Set also λ > 0.…”

Stochastic Interface Models

“…Then, similarly to the proof of Lemma 7.9, one can deduce ρ(J) > 0 from τ wall (J) < 0 and this completes the proof of Theorem 7.7-(2). Velenik [249] discussed the delocalization of interfaces above a wall in a complete wetting regime, and in an external field. Remark 7.7.…”