Critical dynamics of random-field Ising systems with conserved order parameter

Motivated by recent experiments on critical binary fluid mixtures in porous media, the dynamics of random-field Ising systems with conserved order parameter are considered. In the one-phase regime a new dynamic crossover length lₓ is found: for q{}qₓ=2{π}/lₓ the temporal decay of S(q,t) is well approximated by a single exponential whose decay rate is determined by diffusive dynamics, while for q{}qₓ the temporal decay has a strongly nonexponential component, reflecting the activated dynamics of this system. As the ordering transition is approached, this dynamic length lₓ diverges as lₓ{~}exp(cξ^ψ), where {ξ} is the static correlation length, and the activation free-energy barriers are of order cTξ^ψ (T being the temperature and c a nonuniversal constant).