The physics of disordered elastic systems is relevant for a wide range of physical situations, such as vortex lattices in superconductors, charge density waves, domain wall in magnets… In these systems, the competition between elasticity and disorder leads to pinning and glassy behavior. Therefore one expects non-equilibrium effects, as commonly observed in glassy systems.
I will focus on a particular instance of these disordered models in two dimensions, characterized by a logarithmic (therefore called marginal) free energy landscape. Using dynamical Renormalization Group (RG) approaches, including Exact RG Equation and Functional RG, we have recently obtained a rather detailed analytical description of the non equilibrium relaxational dynamics of this system in various temperature regimes.
I will also present a numerical study of these aging phenomena, which allows for a quantitative comparison with analytical predictions. This furthermore suggests an aging scenario based on a growing length scale, which we tried to identify in real space, taking advantage of an existing algorithm to compute exactly the Ground State of this 2D disordered system.

Universitat des Saarlandes, Saarbrucken, Germany