Equilibrium andageing dynamics of simple models for glasses

Abstract

We analyse the properties of the energy landscape of finite-size fully connected p-spin-like models. In thethermodynamic limit the high-temperature phase is described by theschematic mode-coupling theory of supercooled liquids. In thislimit, the barriers between different basins are infinite below thecritical dynamical temperature at which the ergodicity is broken ininfinite time. We show that finite-size fully connectedp-spin-like models, where activated processes are possible, exhibit properties typical of real supercooled liquid when both arenear the critical glass transition. Our results support theconclusion that fully connected p-spin-like models are the naturalstatistical mechanical models for studying the glass transition insupercooled liquids.