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

Abstract

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 $l_x$ is found: for q≪$q_x$=2π/$l_x$ 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≳$q_x$ the temporal decay has a strongly nonexponential component, reflecting the activated dynamics of this system. As the ordering transition is approached, this dynamic length $l_x$ diverges as $l_x$∼exp(c${\xi }^{\psi }$), where ξ is the static correlation length, and the activation free-energy barriers are of order cT${\xi }^{\psi }$ (T being the temperature and c a nonuniversal constant).