Interfaces are part of our everyday life. With scales ranging from nanometers to kilometers, these objects emerge in many different contexts and can give us information about the whole system by just observing a small part of it.
A domain is defined as a portion of the system where the main features of the system are homogeneous or in the same state. An interface of a domain is defined as the region where a system changes from one state to a different one. In the figure I show two examples: a cell colony where the interface is defined as the colony boundary, and a ferromagnet where the interface is the region where the magnetization changes smoothly from one direction (gray) to the opposite one (black).
The framework of Disordered Elastic Systems is a very powerful tool that allows us to do very precise analytical calculations to predict how interfaces will react under different circumstances. It is up to now one of the most successful tools to treat interfaces analytically.
On a different description level, Ginzburg-Landau models had served as a fantastic tool to describe bulk and domain properties. With this description, we can capture many features of interfaces observed experimentally like bubbles, overhangs, and strong pinning centers. But analytical calculations are almost impossible to handle at this level. A connection between this description and the framework of disordered elastic systems will then be useful to extend the theory beyond the elastic approximation.
For centuries many people did huge efforts to connect bulk to interface dynamics, and many researchers were successful in pursuing such a task. However, nobody knew how to do this connection or model reduction in presence of disorder. All the connections are only valid for clean systems.
Disorder plays a key role in all systems.
Geometrical and dynamical properties of interfaces change drastically in presence of disorder. For example, in absence of disorder, an interface under the effects of a force will react linearly: it will acquire a velocity that will be directly proportional to the applied force. In presence of disorder, this is not the case at all. Many other regimes arise. For example, the creep regime. In this regime, the interface velocity is highly non-linear and displays a stretched exponential behavior as a function of the magnitude of the applied field with a characteristic universal exponent. In the framework of disordered elastic systems theory, this universal exponent is directly related to the roughness exponent characterizing the domain wall geometry.
Theoretical and numerical studies of effects in the creep regime are difficult to tackle due to the glassy nature of the problem. The universality of these phenomena allows statistical-physics minimal models to successfully capture the main features of interfaces in this regime. One great advantage of treating systems through this kind of model is that it allows us to distinguish what are the main physical ingredients responsible for the complex observed behavior.
For the first time, with colleagues we connected the bulk to the interface descriptions in presence of disorder.
We can now use all the resources of the disordered elastic systems framework to treat interfaces in the more complex system.
Main Reference
Nirvana Caballero, E. Agoritsas, V. Lecomte, and Thierry Giamarchi.
From bulk descriptions to emergent interfaces: Connecting the Ginzburg-Landau and elastic-line models