J Phys. IV France 8 (1 998) Exploring the configuration space of gIassy models

We briefly describe some recent developments which allow to probe dynamically as well as statically free-energy landscapes of complex systems. Statically, one studies free-energies associated to constrained Boltzmann measures. Dynamically, one studies the relaxation of the system with particular choices of the initial conditions. We present the results for a particular mean-field spin-glass model. Glasses are long lived off-equilibrium states of matter, to which they correspond metastable regions of the configuration space with exponentially small Boltzmann probability. This can be generica.11 ~ related t o the complexity of the energy landscape, where relaxation can be obstructed by constraints of various nature. In this conditions it is important to consider methods which can provide information about the metastable regions. In order t o do that one can restrict the Boltzmann measure to the limited regions of the configuration space. This is what is commonly done in presence of spontaneous symmetry breaking where one uses some external file to project onto one of the possible phases of the system. Unfortunately, the disordered nature of the glassy phase prevents the direct projection on the metastable regions