Related papers: Computer simulations of the Gardner transition in …
Marginally stable solids have peculiar physical properties that were discovered and analyzed in the context of the jamming transition. We theoretically investigate the existence of marginal stability in a prototypical model for structural…
Despite decades of work, gaining a first-principle understanding of amorphous materials remains an extremely challenging problem. However, recent theoretical breakthroughs have led to the formulation of an exact solution in the mean-field…
The Gardner transition is the transition that at mean-field level separates a stable glass phase from a marginally stable phase. This transition has similarities with the de Almeida-Thouless transition of spin glasses. We have studied a…
One of the most remarkable predictions to emerge out of the exact infinite-dimensional solution of the glass problem is the Gardner transition. Although this transition was first theoretically proposed a generation ago for certain…
The Gardner transition in structural glasses is characterized by full-replica symmetry breaking of the free-energy landscape and the onset of anomalous aging dynamics due to marginal stability. Here we show that this transition also has a…
Recent works on hard spheres in the limit of infinite dimensions revealed that glass states, envisioned as meta-basins in configuration space, can break up in a multitude of separate basins at low enough temperature or high enough pressure,…
We propose a simple theory for the dynamics of model glass-forming fluids, which should be solvable using a mean-field-like approach. The theory is based on transparent physical assumptions, which can be tested in computer simulations. The…
Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of…
In this paper we propose a simple mean-field "toy" model for the liquid-glass phase transition. This is the system of $N$ point-like particles confined in a finite volume of a $D$-dimensional space interacting via infinite-range oscillating…
The study of the properties of glass-forming liquids is difficult for many reasons. Analytic solutions of mean field models are usually available only for systems embedded in a space with an unphysically high number of spatial dimensions;…
In this paper and in the companion one we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems---the overlap field…
In this paper we study the glass transition in a model of identical hard spheres, focusing on the two dimensional case. In the mean-field limit the model exhibits an ideal glass transition of the same nature of that found in discontinuous…
Although glass phases are found in various soft matter systems ubiquitously, we are still far from a complete understanding of them. The concept of marginal stability predicted by infinite-dimensional mean-field theories is drawing…
We study Harmonic Soft Spheres as a model of thermal structural glasses in the limit of infinite dimensions. We show that cooling, compressing and shearing a glass lead to a Gardner transition and, hence, to a marginally stable amorphous…
The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics the same way the random energy model clarifies spin glass behavior would…
We construct a mean field theory for the lattice model of a structural glass and solve it using the replica method and one step replica symmetry breaking ansatz; this theory becomes exact in the limit of infinite dimensions. Analyzing…
Apparent critical phenomena, typically indicated by growing correlation lengths and dynamical slowing-down, are ubiquitous in non-equilibrium systems such as supercooled liquids, amorphous solids, active matter and spin glasses. It is often…
The low-temperature phase of discontinuous mean-field spin glasses is generally described by a one-step replica symmetry breaking (1RSB) Ansatz. The Gardner transition, i.e. a very-low-temperature phase transition to a full replica symmetry…
We introduce a family of glassy models having a parameter, playing the role of an interaction range, that may be varied continuously to go from a system of particles in d dimensions to a mean-field version of it. The mean-field limit is…
We numerically analyse the landscape governing the evolution of the vibrational dynamics of hard disk glasses as the density increases towards jamming. We find that the dynamics becomes slow, spatially correlated, and starts to display…