We define restricted ensembles, called pico-canonical ensembles, for a statistical-mechanical description of the metastable and glassy phases. In this approach, time evolution is Markovian, with temperature dependent rates. Below a particular glass temperature, the system is strongly...

To describe the slow dynamics of a system out of equilibrium, but close to a dynamical arrest, we generalise the ideas of previous work to the case where time-translational invariance is broken. We introduce a model of dynamics that is reasonably general, and show how all of the unknown...

We examine the distribution of normal modes in amorphous or glassy materials. Thermodynamical considerations suggest an unusually high density of low-lying states in such materials. Here we inquire into the dynamics, using the appropriate Green functions.

A p-spin interaction Ashkin–Teller spin glass, with three independent Gaussian probability distributions for the exchange interactions, is studied by means of the replica method. A simple phase diagram is obtained within the replica-symmetric approximation, presenting an instability of the...

In this work we present a numerical study of the complex dynamical behavior of the Hopfield model within its retrieval phase. We find that the spin glass solutions that coexist with the retrieval attractors display a rich out of equilibrium dynamics suggesting the presence of a very intricate...

We review the basic ideas which have been developed to characterize geometrically the equilibrium phase transitions. This approach elucidates many concepts like propagation of correlations, upper critical dimensionality, breakdown of hyperscaling, strong universality, and other basic ideas in...