Different scenarios for critical glassy dynamics

We study the role of different terms in the N-body potential of glass-forming systems on the critical dynamics near the glass transition. Using a simplified spin model with quenched disorder, where the different terms of the real N-body potential are mapped into multi-spin interactions, we identified three possible scenarios. For each scenario we introduce a "minimal" model representative of the critical glassy dynamics near, both above and below, the critical transition line. For each "minimal" model we discuss the low-temperature equilibrium dynamics.