Equilibrium and ageing dynamics of simple models for glasses

We analyse the properties of the energy landscape of finite-size fully conn ected p-spin-like models. In the thermodynamic limit the high-temperature p hase is described by the schematic mode-coupling theory of supercooled liqu ids. In this limit, the barriers between different basins are infinite belo w the critical dynamical temperature at which the ergodicity is broken in i nfinite 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 re sults support the conclusion that fully connected p-spin-like models are th e natural statistical mechanical models for studying the glass transition i n supercooled liquids.