It has recently become possible to prepare ultrastable glassy materials characterised by structural relaxation times which vastly exceed the duration of any feasible experiment. Similarly, new algorithms have led to the production of ultrastable computer glasses. Is it possible to obtain a reliable estimate of a structural relaxation time that is too long to be measured? We review, organise, and critically discuss various methods to estimate very long relaxation times. We also perform computer simulations of three dimensional ultrastable hard spheres glasses to test and quantitatively compare some of these methods for a single model system. The various estimation methods disagree significantly and it is not yet clear how to accurately estimate extremely long relaxation times.

We devise a generic strategy and simple numerical models for multi-component metallic glasses for which the swap Monte Carlo algorithm can produce highly stable equilibrium configurations equivalent to experimental systems cooled more than $10^7$ times slower than in conventional simulations. This paves the way for a deeper understanding of thermodynamic, dynamic, and mechanical properties of metallic glasses. As a first application, we extend configurational entropy measurements down to the experimental glass temperature, and demonstrate a qualitative evolution of the mechanical response of metallic glasses of increasing stability towards brittleness.

Finite-dimensional signatures of spinodal criticality are notoriously difficult to come by. The dynamical transition of glass-forming liquids, first described by mode-coupling theory, is a spinodal instability preempted by thermally activated processes that also limit how close the instability can be approached. We combine numerical tools to directly observe vestiges of the spinodal criticality in finite-dimensional glass formers. We use the swap Monte Carlo algorithm to efficiently thermalise configurations beyond the mode-coupling crossover, and analyze their dynamics using a scheme to screen out activated processes, in spatial dimensions ranging from $d=3$ to $d=9$. We observe a strong softening of the mean-field square-root singularity in $d=3$ that is progressively restored as $d$ increases above $d=8$, in surprisingly good agreement with perturbation theory.

We use computer simulations to investigate the extended phase diagram of a supercooled liquid linearly coupled to a quenched reference configuration. An extensive finite-size scaling analysis demonstrates the existence of a random-field Ising model (RFIM) critical point and of a first-order transition line, in agreement with field-theoretical approaches. The dynamics in the vicinity of this critical point resembles the peculiar activated scaling of RFIM-like systems, and the overlap autocorrelation displays a logarithmic stretching. Our study firmly establishes the RFIM criticality in three-dimensional supercooled liquids at equilibrium.

The overlap, or similarity, between liquid configurations is at the core of the mean-field description of the glass transition, and remains a useful concept when studying three-dimensional glass-forming liquids. In liquids, however, the overlap involves a tolerance, typically of a fraction $a/\sigma$ of the inter-particle distance, associated with how precisely similar two configurations must be for belonging to the same physically relevant "state". Here, we systematically investigate the dependence of the overlap fluctuations and of the resulting phase diagram when the tolerance is varied over a large range. We show that while the location of the dynamical and thermodynamic glass transition (if present) are independent of $a/\sigma$, that of the critical point associated with a transition between a low- and a high-overlap phases in the presence of an applied source nontrivially depends on the value of $a/\sigma$. We rationalize our findings by using liquid-state theory and the hypernetted chain (HNC) approximation for correlation functions. In addition, we confirm the theoretical trends by studying a three-dimensional glass-former by computer simulations. We show in particular that a specific choice of $a/\sigma$ maximizes the temperature of the critical point, pushing it up in a liquid region where viscosity is low and computer investigations are easier due to a significantly faster equilibration.

We numerically study yielding in two-dimensional glasses which are generated with a very wide range of stabilities by swap Monte-Carlo simulations and then slowly deformed at zero temperature. We provide strong numerical evidence that stable glasses yield via a nonequilibrium discontinuous transition in the thermodynamic limit. A critical point separates this brittle yielding from the ductile one observed in less stable glasses. We find that two-dimensional glasses yield similarly to their three-dimensional counterparts but display larger sample-to-sample disorder-induced fluctuations, stronger finite-size effects, and rougher spatial wandering of the observed shear bands. These findings strongly constrain effective theories of yielding.

Amorphous packings prepared in the vicinity of the jamming transition play a central role in theoretical studies of the vibrational spectrum of glasses. Two mean-field theories predict that the vibrational density of states $g(\omega)$ obeys a characteristic power law, $g(\omega)\sim\omega^2$, called the non-Debye scaling in the low-frequency region. Numerical studies have however reported that this scaling breaks down at low frequencies, due to finite dimensional effects. In this study, we prepare amorphous packings of up to $128000$ particles in spatial dimensions from $d=3$ to $d=9$ to characterise the range of validity of the non-Debye scaling. Our numerical results suggest that the non-Debye scaling is obeyed down to a frequency that gradually decreases as $d$ increases, and possibly vanishes for large $d$, in agreement with mean-field predictions. We also show that the prestress is an efficient control parameter to quantitatively compare packings across different spatial dimensions.