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 $d<\mathrm{}5\mathrm{}$, the interface will move only if a force beyond a finite depinning threshold $F_c\sim h^{\frac{4}{\mathrm{}(5-d)\mathrm{}}}$ 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 $R_c\sim \frac{1}{h^{\frac{4}{\mathrm{}(5-d)\mathrm{}}}}$ for the average radius of curvature $R$ of the domain walls. If $R>\mathrm{}{R}_c$, the domain structure is frozen. If $R<\mathrm{}{R}_c$, the domain structure evolves until $R\sim R_c$.