Equilibrium and ageing dynamics of simple models for glasses

We analyse the properties of the energy landscape of finite-size fully connected p-spin-like models. In the thermodynamic limit the high-temperature phase is described by the schematic mode-coupling theory of supercooled liquids. In this limit, the barriers between different basins are infinite below the critical dynamical temperature at which the ergodicity is broken in infinite time. We show that finite-size fully connected p-spin-like models, where activated processes are possible, exhibit properties typical of real supercooled liquid when both are near the critical glass transition. Our results support the conclusion that fully connected p-spin-like models are the natural statistical mechanical models for studying the glass transition in supercooled liquids.