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Controlling interfaces is highly relevant from a technological point of view.However, their rich and complex behavior makes them very difficult to describetheoretically, and hence to predict. In this work, we establish a procedure toconnect two levels of descriptions of interfaces: for a bulk description, weconsider a two-dimensional Ginzburg-Landau model evolving with a Langevinequation, and boundary conditions imposing the formation of a rectilineardomain wall. At this level of description no assumptions need to be done overthe interface, but analytical calculations are almost impossible to handle. Ona different level of description, we consider a one-dimensional elastic linemodel evolving according to the Edwards-Wilkinson equation, which only allowsone to study continuous and univalued interfaces, but which was up to now oneof the most successful tools to treat interfaces analytically. To establish theconnection between the bulk description and the interface description, wepropose a simple method that applies both to clean and disordered systems. Weprobe the connection by numerical simulations at both levels, and oursimulations, in addition to making contact with experiments, allow us to testand provide insight to develop new analytical approaches to treat interfaces.

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