The randomly driven Ising ferromagnet: I. General formalism and mean-fieldtheory

We consider the behaviour of an Ising ferromagnet obeying the Glauber dynam ics under the influence of a fast-switching, random external field. After i ntroducing a general formalism for describing such systems, we consider her e the mean-field theory. A novel type of first-order phase transition relat ed to spontaneous symmetry breaking and dynamic freezing is found. The none quilibrium stationary state has a complex structure, which changes as a fun ction of parameters from a singular-continuous distribution with Euclidean or fractal support to an absolutely continuous one. These transitions are r eflected in both finite size effects and sample-to-sample fluctuations.