Related papers: Matrix models as solvable glass models
We consider particles on a one-dimensional lattice whose evolution is governed by nearest-neighbor interactions where particles that have reached size zero are removed from the system. Concentrating on configurations with infinitely many…
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…
We show numerically that a three-dimensional model for structural glass displays aging, rejuvenation and memory effects when submitted to a temperature cycle. These effects indicate that the free energy landscape of structural glasses may…
The dynamical behavior of a kind of models with hierarchically constrained dynamics is investigated. The models exhibit many properties resembling real structural glasses. In particular, we focus on the study of time-dependent temperature…
The glass transition of mesoscopic charged particles in two-dimensional confinement is studied by mode-coupling theory. We consider two types of effective interactions between the particles, corresponding to two different models for the…
We review the most striking experimental results on aging in a variety of disordered systems, which reveal similar features but also important differences. We argue that a generic model that reproduce many of these features is that of {\it…
Integrability conditions for systems of bosons or fermions with seniority conserving hamiltonians are derived. The conditions are shown to be invariant under a large class of transformations of the interaction matrix elements. Previously…
In a $p$-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change in the course of time. The spins are coupled to a heat bath with temperature $T$, while the coupling constants are coupled to a bath…
We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…
We offer an alternative real-space description, based purely on activated processes, for the understanding of relaxation dynamics in hierarchical landscapes. To this end, we use the cluster model, a coarse-grained lattice model of a jammed…
We study the dynamics of a dilute spherical model with two body interactions and random exchanges. We analyze the Langevin equations and we introduce a functional variational method to study generic dilute disordered models. A crossover…
We investigate the quenching process in lattice systems with short range interaction and several crystalline states as ground states. We consider in particular the following systems on square lattice: - hard particle (exclusion) model; - q…
We introduce a new toy model for the study of glasses: the hard-matrix model (HMM). This may be viewed as a single particle moving on $\mathrm{SO}(N)$, where there is a potential proportional to the 1-norm of the matrix. The ground states…
A model glass with fast and slow processes is studied. The statics is simple and the facilitated slow dynamics is exactly solvable. The main features of a fragile glass take place: Kauzmann transition, Vogel-Fulcher law, Adam-Gibbs relation…
We review recent theoretical progress on glassy dynamics, with special emphasis on the importance and universality of the ``aging regime'', which is relevant to many experimental situations. The three main subjects which we address are: (i)…
The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant…
A disordered system is denominated `annealed' when the interactions themselves may evolve and adjust their values to lower the free energy. The opposite (`quenched') situation when disorder is fixed, is the one relevant for physical…
A disordered spin glass model where both static and dynamical properties depend on macroscopic magnetizations is presented. These magnetizations interact via random couplings and, therefore, the typical quenched realization of the system…
Excitations of disordered systems such as glasses are of fundamental and practical interest but computationally very expensive to solve. Here we introduce a technique for modeling these excitations in an infinite disordered medium with a…
Soft matter systems are common in nature and make up nearly all the essential components necessary for life, from cells to the organelles within those cells. The ability of these soft materials to deform is crucial for the proper…