Dynamics of structural models with a long-range interaction: Glassy versusnonglassy behavior

By making use of the Langevin dynamics and its generating functional (GF) f ormulation, the influence of the long-range nature of the interaction on th e tendency of the glass formation is systematically investigated. In doing so, two types of models are considered: (i) the nondisordered model with a pure repulsive type of interaction, and (ii) the model with a randomly dist ributed strength of interaction (a quenched disordered model). The long-ran ged potential of interaction is scaled with a number of particles N in such a way as to enable for the GF the saddle-point treatment as well as the sy stematic 1/N expansion around it. We show that the nondisordered model has no glass transition, which is in line with the mean-field limit of the mode -coupling theory (MCT) predictions. On the other hand, the model with a lon g-range interaction that has a quenched disorder leads to MC equations whic h are generic for the p-spin glass model and polymeric manifold in a random media.