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An analytically tractable model is introduced which exhibits both, a glass--like freezing transition, and a collection of double--well configurations in its zero--temperature potential energy landscape. The latter are generally believed to…
Our goal is to discuss in detail the calculation of the mean number of stationary points and minima for random isotropic Gaussian fields on a sphere as well as for stationary Gaussian random fields in a background parabolic confinement.…
We introduce a family of glassy models having a parameter, playing the role of an interaction range, that may be varied continuously to go from a system of particles in d dimensions to a mean-field version of it. The mean-field limit is…
We propose a simple theory for the dynamics of model glass-forming fluids, which should be solvable using a mean-field-like approach. The theory is based on transparent physical assumptions, which can be tested in computer simulations. The…
Aspects of the dynamical glass transition are considered within a mean field spin glass model. At the dynamical transition the the system condenses in a state of lower entropy. The difference, the information entropy or complexity, is…
Activated dynamics in a glassy system undergoing steady shear deformation is studied by numerical simulations. Our results show that the external driving force has a strong influence on the barrier crossing rate, even though the reaction…
We study the off equilibrium dynamics of a mean field disordered systems which can be interpreted both as a long range interaction spin glass and as a particle in a random potential. The statics of this problem is well known and exhibits a…
We will review some of the theoretical progresses that have been recently done in the study of slow dynamics of glassy systems: the general techniques used for studying the dynamics in the mean field approximation and the emergence of a…
We present a simple mathematical model of glassy dynamics seen as a random walk in a directed, weighted network of minima taken as a representation of the energy landscape. Our approach gives a broader perspective to previous studies…
The dynamical transition occurring in spin-glass models with one step of Replica-Symmetry-Breaking is a mean-field artifact that disappears in finite systems and/or in finite dimensions. The critical fluctuations that smooth the transition…
In these lectures I will present an introduction to the modern way of studying the properties of glassy systems. I will start from soluble models of increasing complications, the Random Energy Model, the $p$-spins interacting model and I…
On the basis of long simulations of a binary mixture of soft spheres just below the glass transition, we make an exploratory study of the activated processes that contribute to the dynamics. We concentrate on statistical measures of the…
Facilitated spin models were introduced some decades ago to mimic systems characterized by a glass transition. Recent developments have shown that a class of facilitated spin models is also able to reproduce characteristic signatures of the…
We present a three-dimensional lattice-gas model with trivial thermodynamics, but nontrivial dynamics. The model is characterized by each particle having its own random energy landscape. The equilibrium dynamics of the model were…
We propose a simple dynamical model for a glass transition. The dynamics is described by a Langevin equation in a piecewise parabolic free energy landscape, modulated by a temperature dependent overall curvature. The zero-curvature point…
The mean-field theory of Kinetically-Constrained-Models is developed by considering the Fredrickson-Andersen model on the Bethe lattice. Using certain properties of the dynamics observed in actual numerical experiments we derive asymptotic…
Aim of this work is not trying to explore a macroscopic behavior of some recent model in statistical mechanics but showing how some recent techniques developed within the framework of spin glasses do work on simpler model, focusing on the…
In order to study the activated dynamics of mean-field glasses, which takes place on times of order exp(N), where N is the system size, we introduce a new model, the Correlated Random Energy Model (CREM), that allows for a smooth…
We present a simple mathematical framework for the description of the dynamics of glassy systems in terms of a random walk in a complex energy landscape pictured as a network of minima. We show how to use the tools developed for the study…
Slow relaxation and glassiness have been the focus of extensive research attention, along with popular and technological interest, for many decades. While much understanding has been attained through mean-field and mode-coupling models,…