Glassy dynamics of kinetically constrained models

We review recent findings on spin glass models. Both the equilibrium properties and the dynamic properties are covered. We focus on progress in theoretical, in particular numerical, studies, while its relationship to real magnetic materials is also mentioned.

The ultraslow dynamics of glass-formers has been explained by two views considered as mutually exclusive: one invokes locally hindered mobility, the other rests on the complexity of the configuration space. Here we demonstrate that the evolution responds strongly to the details of the dynamics by changing the speed of time-flow: it has time-reparametrization softness. This finding reconciles both views: while local constraints reparametrize the flow of time, the global landsc...

This review reports on the research done during the past years on violations of the fluctuation-dissipation theorem (FDT) in glassy systems. It is focused on the existence of a quasi-fluctuation-dissipation theorem (QFDT) in glassy systems and the currently supporting knowledge gained from numerical simulation studies. It covers a broad range of non-stationary aging and stationary driven systems such as structural-glasses, spin-glasses, coarsening systems, ferromagnetic model...

We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the relaxation dynamics that arise in comparison to systems evolving via classical rate equations. In particular, we focus on a scenario where both quantum and classical dissipative evolution lead to a stationary state with the same values of diagonal ...

Kinetically constrained models (KCM) are reversible interacting particle systems on $\mathbb Z^d$ with continuous time Markov dynamics of Glauber type, which represent a natural stochastic (and non-monotone) counterpart of the family of cellular automata known as $\mathcal U$-bootstrap percolation. KCM also display some of the peculiar features of the so-called "glassy dynamics", and as such they are extensively used in the physics literature to model the liquid-glass transit...

In this paper we consider in detail the properties of dynamical heterogeneity in lattice glass models (LGMs). LGMs are lattice models whose dynamical rules are based on thermodynamic, as opposed to purely kinetic, considerations. We devise a LGM that is not prone to crystallization and displays properties of a fragile glass-forming liquid. Particle motion in this model tends to be locally anisotropic on intermediate time scales even though the rules governing the model are is...

The physics of glasses can be studied from many viewpoints, from material scientists interested in the development of new materials to statistical physicists inventing new theoretical tools to deal with disordered systems. In these lectures I described a variety of physical phenomena observed in actual glassy materials, from disordered magnetic systems to soft gels. Despite the very large gap between experimental and numerical time windows, I showed that computer simulations ...

We consider in parallel three one-dimensional spin models with kinetic constraints: the paramagnetic constrained Ising chain, the ferromagnetic Ising chain with constrained Glauber dynamics, and the same chain with constrained Kawasaki dynamics. At zero temperature the dynamics of these models is fully irreversible, leading to an exponentially large number of blocked states. Using a mapping of these spin systems onto sequential adsorption models of, respectively, monomers, di...

Contribution presented by Eric Vincent in the Conference `Complex Behaviour of Glassy Systems', Sitges, Barcelona, Spain, June, 1996. It contains a review of the experimental results on Slow dynamics and aging in spin-glasses. It also presents their comparison with recent theoretical developments in the description of the out of equilibrium dynamics of disordered systems; namely, the trap model and the mean-field theory.

In this work a short overview of the development of spin glass theories, mainly long and short range Ising models, are presented.