Interfacial roughening in field theory

TL;DR

This paper derives analytical expressions for interface roughening in the Landau-Ginzburg model, providing a first-principles field theory approach that avoids ad hoc cut-offs used in traditional capillary wave models.

Contribution

It introduces a renormalized field theory framework to analyze interface roughening, yielding finite, explicit formulas for interface width and profile.

Findings

Analytical expressions for interface width and profile are obtained.

Results depend on the renormalized coupling constant.

Expressions are valid in the scaling region.

Abstract

In the rough phase, the width of interfaces separating different phases of statistical systems increases logarithmically with the system size. This phenomenon is commonly described in terms of the capillary wave model, which deals with fluctuating, infinitely thin membranes, requiring ad hoc cut-offs in momentum space. We investigate the interface roughening from first principles in the framework of the Landau-Ginzburg model, that is renormalized field theory, in the one-loop approximation. The interface profile and width are calculated analytically, resulting in finite expressions with definite coefficients. They are valid in the scaling region and depend on the known renormalized coupling constant.