Wetting of gradient fields: pathwise estimates

TL;DR

This paper investigates the wetting transition in gradient interface models, providing pathwise estimates that demonstrate interface localization in partial wetting regimes and analyzing delocalization near the transition point.

Contribution

It introduces pathwise estimates for interface localization and delocalization in gradient models, utilizing reflection positivity and chessboard estimates.

Findings

Interface remains localized in the partial wetting regime.

Interface delocalizes as the wetting transition is approached.

Utilizes reflection positivity as a key analytical tool.

Abstract

We consider the wetting transition in the framework of an effective interface model of gradient type, in dimension 2 and higher. We prove pathwise estimates showing that the interface is localized in the whole thermodynamically-defined partial wetting regime considered in earlier works. Moreover, we study how the interface delocalizes as the wetting transition is approached. Our main tool is reflection positivity in the form of the chessboard estimate.