Fluctuating Interfaces, Surface Tension, and Capillary Waves: An Introduction

TL;DR

This paper introduces modern theories of interfacial fluctuations, surface tension, and capillary waves, reviewing transfer matrix properties, roughening transitions, and differences between rigid and rough interfaces in lattice models.

Contribution

It provides a comprehensive overview of interfacial fluctuation theories, including transfer matrix analysis and the distinction between rigid and rough interfaces in three-dimensional models.

Findings

Transfer matrix spectrum properties reveal differences between rigid and rough interfaces.

The roughening transition significantly affects interfacial fluctuation behavior.

Surface tension and stiffness are key parameters in capillary wave models.

Abstract

We present an introduction to modern theories of interfacial fluctuations and the associated interfacial parameters: surface tension and surface stiffness, as well as their interpretation within the capillary wave model. Transfer matrix spectrum properties due to fluctuation of an interface in a long-cylinder geometry are reviewed. The roughening transition and properties of rigid interfaces below the roughening temperature in 3d lattice models are surveyed with emphasis on differences in fluctuations and transfer matrix spectral properties of rigid vs. rough interfaces.