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 qqx=2/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 qqx 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 lxexp(c), where is the static correlation length, and the activation free-energy barriers are of order cT (T being the temperature and c a nonuniversal constant).