The field‐theoretic description of dynamics of interfaces in disordered media

The time evolution of an interface in a disordered media is described by using the propagator method. The method enables one to represent the perturbation expansions of different quantities characterizing the interface by means of diagrams which are familiar from the field theory. By the analysis of the divergences in the vicinity of the critical dimension d c = 4 we found that the regularization of the theory demands the renormalization of the mobility and all moments of the disorder correlator excepting the zero one. The renormalization group (RG) calculations of the average velocity of the interface, the roughness, and the functional RG equation of the disorder correlator are presented to order ϵ = 4 ‐ d . The latter coincides with the result obtained by D. S. Fisher in the equilibrium case. The RG equations have a pole at the value of the driving force, which coincides with the value of the threshold below which the interface becomes pinned as predicted by Bruinsma and Aeppli. The behavior of the mobility in the vicinity of the pole is discussed.