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

Abstract

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 ${F}_{c}\ensuremath{\sim}{h}^{\frac{4}{(5\ensuremath{-}d)}}$ 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 ${R}_{c}\ensuremath{\sim}\frac{1}{{h}^{\frac{4}{(5\ensuremath{-}d)}}}$ for the average radius of curvature $R$ of the domain walls. If $R>{R}_{c}$, the domain structure is frozen. If $R<{R}_{c}$, the domain structure evolves until $R\ensuremath{\sim}{R}_{c}$.