Interface Motion and Nonequilibrium Properties of the Random-Field Ising Model

The dynamics of a continuum interface model in a random medium are studied and the results applied to the random-field Ising model. We find that if the dimensionality $d<5$, the interface will move only if a force beyond a finite depinning threshold Fc~h^4(5-d) is applied, where h is the random field strength. Thus, when the random-field Ising model is quenched to low temperatures, there is a critical value Rc~1h^4(5-d) for the average radius of curvature R of the domain walls. If R>Rc, the domain structure is frozen. If R<Rc, the domain structure evolves until R~Rc.