  We analyze numerically a moving interface in the random-field Ising model
which is driven by a magnetic field. Without thermal fluctuations the system
displays a depinning phase transition, i.e., the interface is pinned below a
certain critical value of the driving field. For finite temperatures the
interface moves even for driving fields below the critical value. In this
so-called creep regime the dependence of the interface velocity on the
temperature is expected to obey an Arrhenius law. We investigate the details of
this Arrhenius behavior in two and three dimensions and compare our results
with predictions obtained from renormalization group approaches.
