Dynamics and melting of stripes, crystals, and bubbles with quenched disorder

Two-dimensional systems in which there is a competition between long-range repulsion and short-range attraction exhibit a remarkable variety of patterns such as stripes, bubbles, and labyrinths. Such systems include magnetic films, Langmuir monolayers, polymers, gels, water–oil mixtures, and two-dimensional electron systems. In many of these systems quenched disorder from the underlying substrate may be present. We examine the dynamics and stripe formation in the presence of both an applied dc drive and quenched disorder. When the disorder strength exceeds a critical value, an applied dc drive can induce a dynamical stripe ordering transition to a state that is more ordered than the originating undriven, unpinned pattern. We also consider the melting transition of the different patterns.