Glassy dynamics of kinetically constrained models

We present a detailed physical analysis of the dynamical glass-jamming transition which occurs for the so called Knight models recently introduced and analyzed in a joint work with D.S.Fisher \cite{letterTBF}. Furthermore, we review some of our previous works on Kinetically Constrained Models. The Knights models correspond to a new class of kinetically constrained models which provide the first example of finite dimensional models with an ideal glass-jamming transition. Thi...

We consider the dynamics of spin facilitated models of glasses in the non-equilibrium aging regime following a sudden quench from high to low temperatures. We briefly review known results obtained for the broad class of kinetically constrained models, and then present new results for the behaviour of the one-spin facilitated Fredrickson-Andersen and East models in various spatial dimensions. The time evolution of one-time quantities, such as the energy density, and the detail...

I propose a new method to study computationally difficult problems. I consider a new system, larger than the one I want to simulate. The original system is recovered by imposing constraints on the large system. I simulate the large system with the hard constraints replaced by soft constraints. I illustrate the method in the case of the ferromagnetic Ising model and in the case the three dimensional spin-glass model. I show that in both models the phases of the soft problem ha...

We study the relaxational dynamics of the one-spin facilitated Ising model introduced by Fredrickson and Andersen. We show the existence of a critical time which separates an initial regime in which the relaxation is exponentially fast and aging is absent from a regime in which relaxation becomes slow and aging effects are present. The presence of this fast exponential process and its associated critical time is in agreement with some recent experimental results on fragile gl...

Motivated by the concept of geometrical frustration, we introduce a class of statistical mechanics lattice models for the glass transition. Monte Carlo simulations in three dimensions show that they display a dynamical glass transition which is very similar to that observed in other off-lattice systems and which does not depend on a specific dynamical rule. Whereas their analytic solution within the Bethe approximation shows that they do have a discontinuous glass transition ...

The purpose of this manuscript is to review my recent activity on three main research topics. The first concerns the nature of low temperature amorphous solids and their relation with the spin glass transition in a magnetic field. This is the subject of the first chapter where I discuss a new model, the KHGPS model, which allows to make some progress. In the second chapter I review a second research line that concerns the study of the rigidity/jamming transitions in particle ...

We review the field of the glass transition, glassy dynamics and aging from a statistical mechanics perspective. We give a brief introduction to the subject and explain the main phenomenology encountered in glassy systems, with a particular emphasis on spatially heterogeneous dynamics. We review the main theoretical approaches currently available to account for these glassy phenomena, including recent developments regarding mean-field theory of liquids and glasses, novel comp...

Kinetically constrained spin models are schematic coarse-grained models for the glass transition which represent an efficient theoretical tool to study detailed spatio-temporal aspects of dynamic heterogeneity in supercooled liquids. Here, we study how spatially correlated dynamic domains evolve with time and compare our results to various experimental and numerical investigations. We find that strong and fragile models yield different results. In particular, the lifetime of ...

We numerically study the zero-temperature relaxation dynamics of several glass-forming models to their inherent structures, following quenches from equilibrium configurations sampled across a wide range of initial temperatures. In a mean-field Mari-Kurchan model, we find that relaxation changes from a power-law to an exponential decay below a well-defined temperature, consistent with recent findings in mean-field $p$-spin models. By contrast, for finite-dimensional systems, t...

We review an scenario for the non-equilibrium dynamics of glassy systems that has been motivated by the exact solution of simple models. This approach allows one to set on firmer grounds well-known phenomenological theories. The old ideas of entropy crisis, fictive temperatures, free-volume... have clear definitions within these models. Aging effects in the glass phase are also captured. One of the salient features of the analytic solution, the breakdown of the fluctuation-di...