Day 2 - Talks

Developing a theory of activated dynamics is one of the most challenging problems of disordered systems. Activated glassy dynamics is central in many different contexts both in physics and beyond, e.g. in computer science and biology. In this talk, after a general introduction, I will describe recent research works aimed at characterising the activated dynamics of mean-field glassy systems. In particular I will discuss numerical results on the random energy model and variants, and analytical results on the organization of barriers in the p-spin spherical model.

Here, we report a study of the linear responses of an aging Ising spin-glass to an external magnetic field, carried out by means of large-scale simulations on Janus and Janus II. We show that linear responses relate experimentally relevant quantities with the experimentally unreachable low-temperature equilibrium phase. We have performed an accurate computation of the non-equilibrium fluctuation-dissipation ratio. This ratio (computed for finite times on very large, effectively infinite, systems) is compared with the equilibrium probability distribution of the spin overlap for finite sizes. The resulting quantitative statics-dynamics dictionary, based on observables that can be measured with current experimental methods, could allow the experimental exploration of important features of the spin-glass phase without uncontrollable extrapolations to infinite times or system sizes.

As a first step, we consider the time growth of the size of the spin-glass domains, ξ. Excellent experimental measurements of this growth, as characterized by the so-called dynamic exponent, are now possible in films. These improved experimental studies show that the dynamic exponent is significantly larger than anticipated by previous experiments and simulations. Our new computation of the dynamic exponent finds a mild dependence on ξ. A modest extrapolation to ξ similar to the thickness of the experimental films produces a dynamic exponent in fair agreement with [Q. Zhai et al., Phys. Rev. B 95, 054304 (2017)].

Glassy dynamics has long been recognized as having a time-reparametrization (almost) invariance, physically related to the diverging susceptibility of the relaxation timescale of these systems with respect to perturbations, such as shear. Zero temperature entropy also appears naturally, once one considers the generator of the dynamics, as a consequence of the multiplicity of metastable states. The developments around the SYK model offer the hope importing some ideas from the Field Theory community.

Swap algorithms can shift the glass transition to lower temperatures, a recent unexplained observation constraining the nature of this phenomenon. Here we show that swap dynamics is governed by an effective potential describing both particle interactions as well as their ability to change size. Requiring its stability is more demanding than for the potential energy alone. This result implies that stable configurations appear at lower energies with swap dynamics, and thus at lower temperatures when the liquid is cooled. We test these predictions numerically and discuss the implications of our findings for the glass transition. These results are extended to the case of hard spheres where swap is argued to destroy metastable states of the free energy coarse grained on vibrational timescales. Our analysis unravels the soft elastic modes responsible for the speed-up induced by swap, and allows us to predict the structure and the vibrational properties of glass configurations reachable with swap. In particular, for continuously polydisperse systems we predict the jamming transition to be dramatically altered, as we confirm numerically. A surprising practical outcome of our analysis is a new algorithm that generates ultrastable glasses by a simple descent in an appropriate effective potential.

Many liquids become extremely sluggish upon supercooling. One explanation -- inspired by RSB -- is that an entropy crisis associated with the rarefaction of available states at the Kauzmann temperature makes it increasingly arduous to reach equilibrium. In practice, this gives rise to a glass ceiling temperature, below which equilibration is out of experimental reach. Using a specialized Monte Carlo algorithm, we have recently managed to break the glass ceiling for various model glass formers. In three dimensions, this methodological advance reinforces the relevance of an entropy crisis for understanding glass formation, with a much more precise measure of configurational entropy than previously possible. In two dimensions, by contrast, the results suggest that a Kauzmann temperature sits right at zero temperature. This finding calls for a theoretical explanation and for investigations regarding putative connections with the peculiar dynamics of these liquids.

It was understood long ago that the spin-glass phase is characterised by some "amorphous magnetic order" that cannot be revealed by the linear susceptibility, but that leads to a diverging cubic (and higher order) static susceptibilities. Supercooled liquids are also thought to be made of a (transient) mosaic of small "glassites" where some amorphous order has set in. Correspondingly, non linear susceptibilities should reveal such order at non-zero frequencies. This is indeed borne out by a recent series of dielectric experiments in Saclay and in Augsburg, which broadly confirm the existence of randomly frozen clusters of dipoles, of larger and larger sizes when temperature is decreased. This is in line with thermodynamical theories of the glass transition, such as the RFOT.