Related papers: Glass-like Caging with Random Planes
We examined energy spectrums of some particular systems of binary spins. It is shown that the configuration space can be divided into classes, and in the limit the energy distributions in these classes can be approximated by the normal…
We determine explicit variational expressions for the free energy of mean-field spin glasses in a transversal magnetic field, whose glass interaction is given by a hierarchical Gaussian potential as in Derrida's Generalized Random Energy…
A random matrix approach to glassy physics is introduced. It leads to a class of models which exhibit both, glassy low-temperature phases, and double-- and single-well configurations in their potential energy. The distribution of parameters…
We analyze the properties of a Lennard-Jones system at the level of the potential energy landscape. After an exhaustive investigation of the topological features of the landscape of the systems, obtained studying small size sample, we…
The starting point of the present work is the observation of possible analogies, both at the phenomenological and at the methodological level, between the subcritical transition to turbulence and the glass transition. Having recalled the…
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…
A mean-field model of Ising spin glass with the Hamiltonian being a sum of the infinite-range ferromagnetic and random antiferromagnetic interactions is studied. It is shown that this model has phase transition in external magnetic field…
Spin glasses occupy a unique place in condensed matter: they freeze collectively while remaining struc-turally disordered, and they exhibit slow, history-dependent dynamics that reflect an exceptionally rug-ged free-energy landscape. This…
Facilitated or kinetically constrained spin models (KCSM) are a class of interacting particle systems reversible w.r.t. to a simple product measure. Each dynamical variable (spin) is re-sampled from its equilibrium distribution only if the…
It was recently shown that the real part of the frequency-dependent fluidity for several glass-forming liquids of different chemistry conforms to the prediction of the random barrier model (RBM) devised for ac electrical conduction in…
A longstanding open question in the theory of disordered systems is whether short-range models, such as the random field Ising model or the Edwards-Anderson model, can indeed have the famous properties that characterize mean-field spin…
Spherical spin glasses are canonical models for smooth random functions in high dimensions. In this review, we survey several interrelated lines of research on their geometric structure. We begin with results concerning critical points and…
We propose a connection between self-similar, focusing dynamics in nonlinear partial differential equations (PDEs) and macroscopic dynamic features of the glass transition. In particular, we explore the divergence of the appropriate…
In an effort to understand the glass transition, the dynamics of a non-randomly frustrated spin model has been analyzed. The phenomenology of the spin model is similar to that of a supercooled liquid undergoing the glass transition. The…
Using the inherent structure formalism originally proposed by Stillinger and Weber [Phys. Rev. A 25, 978 (1982)], we generalize the thermodynamics of an energy landscape that has an ideal glass transition and derive the consequences for its…
The free energy of TAP-solutions for the SK-model of mean field spin glasses can be expressed as a nonlinear functional of local terms: we exploit this feature in order to contrive abstract REM-like models which we then solve by a classical…
Recent work suggests that Heisenberg spin glasses may belong to the same universality class than structural glasses. Indeed, finding a lattice equivalent for supercooled liquids would probably allow easier numerical and analytical studies,…
Spin glasses are quintessential examples of complex matter. Although much about their order remains uncertain, abstract models of them inform, e.g., the classification of combinatorial optimization problems, the magnetic ordering in metals…
The spherical mean field approximation of a spin-1 model with p-body quenched disordered interaction is investigated. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the…
Gradient descent dynamics in complex energy landscapes, i.e. featuring multiple minima, finds application in many different problems, from soft matter to machine learning. Here, we analyze one of the simplest examples, namely that of soft…