From bulk descriptions to emergent interfaces: connecting the Ginzburg-Landau and elastic line models

TL;DR

This paper develops a method to connect detailed bulk models of interfaces with simplified elastic line models, enabling better analytical understanding and experimental relevance of complex interface behaviors.

Contribution

It introduces a novel procedure linking Ginzburg-Landau bulk models to elastic line interface models, applicable to both clean and disordered systems.

Findings

Numerical simulations validate the connection between models.

The method applies to disordered and clean systems.

Insights facilitate new analytical approaches for interfaces.

Abstract

Controlling interfaces is highly relevant from a technological point of view. However, their rich and complex behavior makes them very difficult to describe theoretically, and hence to predict. In this work, we establish a procedure to connect two levels of descriptions of interfaces: for a bulk description, we consider a two-dimensional Ginzburg-Landau model evolving with a Langevin equation, and boundary conditions imposing the formation of a rectilinear domain wall. At this level of description no assumptions need to be done over the interface, but analytical calculations are almost impossible to handle. On a different level of description, we consider a one-dimensional elastic line model evolving according to the Edwards-Wilkinson equation, which only allows one to study continuous and univalued interfaces, but which was up to now one of the most successful tools to treat interfaces analytically. To establish the connection between the bulk description and the interface description, we propose a simple method that applies both to clean and disordered systems. We probe the connection by numerical simulations at both levels, and our simulations, in addition to making contact with experiments, allow us to test and provide insight to develop new analytical approaches to treat interfaces.