Interface in presence of a wall. Results from field theory

TL;DR

This paper analytically studies the behavior of interfaces near a wall in three-dimensional statistical systems at phase coexistence, deriving fundamental properties like passage probability and order parameter profiles from field theory.

Contribution

It provides a first-principles analytical approach to interface behavior near walls, including binding transitions, in statistical field theory.

Findings

Derived the passage probability of the interface.

Obtained the order parameter profile near the wall.

Accounted for the binding transition and its key parameter.

Abstract

We consider three-dimensional statistical systems at phase coexistence in the half-volume with boundary conditions leading to the presence of an interface. Working slightly below the critical temperature, where universal properties emerge, we show how the problem can be studied analytically from first principles, starting from the degrees of freedom (particle modes) of the bulk field theory. After deriving the passage probability of the interface and the order parameter profile in the regime in which the interface is not bound to the wall, we show how the theory accounts at the fundamental level also for the binding transition and its key parameter.