Related papers: Marginal Stability in Structural, Spin and Electro…
Marginal stability is the notion that stability is achieved, but only barely so. This property constrains the ensemble of configurations explored at low temperature in a variety of systems, including spin, electron and structural glasses. A…
We investigate the properties of the glass phase of a recently introduced spin glass model of soft spins subjected to an anharmonic quartic local potential, which serves as a model of low temperature molecular or soft glasses. We solve the…
Mechanical deformation of amorphous solids can be described as consisting of an elastic part in which the stress increases linearly with strain, up to a yield point at which the solid either fractures or starts deforming plastically. It is…
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…
A novel form of amorphous matter characterized by marginal stability was recently discovered in the mean-field theory of structural glasses. Using this approach, we provide complete phase diagrams delimiting the location of the marginally…
In this paper we investigate the marginally stable nature of the low-temperature trivial spin glass phase in the spherical $p=2$ spin glass, by perturbing the system with three different kinds of non-linear interactions. In particular, we…
We show marginal stability of near-ground states in spherical spin glasses is equivalent to full replica symmetry breaking at zero temperature near overlap $1$. This connection has long been implicit in the physics literature, which also…
Bethe lattice spins glasses are supposed to be marginally stable, i.e. their equilibrium probability distribution changes discontinuously when we add an external perturbation. So far the problem of a spin glass on a Bethe lattice has been…
Recently, progress has been made in the understanding of anomalous vibrational excitations in amorphous solids. In the lowest-frequency region, the vibrational spectrum follows a non-Debye quartic law, which persists up to zero frequency…
We study networks of coupled bistable elastic elements, recently proposed as a model for crumpled thin sheets. The networks are poised on the verge of a localized instability, and the model allows unique access to both local and global…
An important but little-studied property of spin glasses is the stability of their ground states to changes in one or a finite number of couplings. It was shown in earlier work that, if multiple ground states are assumed to exist, then…
In a recent publication we established an analogy between the free energy of a hard sphere system and the energy of an elastic network [1]. This result enables one to study the free energy landscape of hard spheres, in particular to define…
We introduce a set of theoretical ideas that form the basis for an analytical framework capable of describing nonequilibrium dynamics in glassy systems. We test the resulting scenario by comparing its predictions with numerical simulations…
We use a random pinning procedure to investigate stable glassy states associated with large deviations of the activity in a model glass-former. We pin particles both from active (equilibrium) configurations and from stable (inactive) glassy…
We introduce and prove a novel linear response stability theory for spin glasses. The new stability under suitable perturbation of the equilibrium state implies the whole set of structural identities that characterize the spin glass phase.
We review the physics of jamming from the theoretical, experimental and numerical perspectives. We summarize the mean-field theory of jamming and the marginally stable solid phase, with particular emphasis on the connection with the Replica…
By comparing the response to external strains in metallic glasses and in Lenard-Jones glasses we find a quantitative universality of the fundamental plastic instabilities in the athermal, quasistatic limit. Microscopically these two types…
Dilute magnetic nanoparticle systems exhibit slow dynamics [1] due to a broad distribution of relaxation times that can be traced to a correspondingly broad distribution of particle sizes [1]. However, at higher concentrations interparticle…
We propose an approach toward understanding the spin glass phase at zero and low temperature by studying the stability of a spin glass ground state against perturbations of a single coupling. After reviewing the concepts of flexibility,…
The requirement that packings of hard particles, arguably the simplest structural glass, cannot be compressed by rearranging their network of contacts is shown to yield a new constraint on their microscopic structure. This constraint takes…