Random systems far from equilibrium:
depinning, friction, crack propagation

The equilibrium properties of condensed matter systems depend in general on the scale of observation and on the microscopic details of the systems. Only close to critical points the behaviour becomes scale invariant and universal [1].
In 1992 we investigated the depinning transition of a driven domain wall in an impure ferromagnet at zero temperature and showed that this transition is an example of a critical point far from equilibrium [2]. Here the wall velocity v plays the role of the order parameter.
In [2] we found new scaling laws between the critical exponents which describe the scaling behaviour of the wall close to the depinning theshold.
The critical exponents were calculated in an expansion around the critical dimensionality 4. The analytical work presented in [2] was confirmed by detailed numerical investigations [3].
Domain-wall depinning is a paradigm for other depinning transitions which occur in type-II superconductors, charge density waves, liquid-solid contact lines etc. [4], [5], and has practical consequences e.g. in the switching behaviour of magnetic films [6].
A somewhat related problem - the transition from static to dynamic elastic dry friction between two rough surfaces  - was investigated in [7], where the Amontow law for friction was derived for a simplified statistical model.
Recently we started the investigation of crack propagation in inhomogeneous materials using a crack description by topological defects.
Vortices in type-II superconductors provide a paradigmatic system to study the physics of systems far from equilibrium. Their behavior is extremely rich and includes phenomena such as non-equilibrium phase transitions. For a description of our activities in this context, see our corresponding section vortex matter.