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Simple elastic models of spin-crossover compounds are known empirically to exhibit classical critical behavior. We demonstrate how the long-ranged interactions responsible for this behavior arise naturally upon integrating out mechanical…
We analyze the properties of the energy landscape of {\it finite-size} fully connected $p$-spin-like models. In the thermodynamic limit the high temperature phase is described by the schematic Mode Coupling Theory of super-cooled liquids.…
We present a many body approach for non-equilibrium behavior and self-generated glassiness in strongly correlated quantum systems. It combines the dynamical mean field theory of equilibrium systems with the replica theory for classical…
We analyze the coupled non-linear integro-differential equations whose solutions is the thermodynamical limit of the empirical correlation and response functions in the Langevin dynamics for spherical p-spin disordered mean-field models. We…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
Properties of the free energy landscape in phase space of a dense hard sphere system characterized by a discretized free energy functional of the Ramakrishnan-Yussouff form are investigated numerically. A considerable number of glassy local…
We study the energy-landscape network of Lennard-Jones clusters as a model of a glass forming system. We find the stable basins and the first order saddles connecting them, and identify them with the network nodes and links, respectively.…
We explore Langevin dynamics in the spherical Sherrington-Kirkpatrick model, delving into the asymptotic energy limit. Our approach involves integro-differential equations, incorporating the Crisanti-Horner-Sommers-Cugliandolo-Kurchan…
We present a new method to close the Master Equation representing the continuous time dynamics of Ising interacting spins. The method makes use of the the theory of Random Point Processes to derive a master equation for local conditional…
We have explored a simple microscopic model to simulate a thermally activated rate process where the associated bath which comprises a set of relaxing modes is not in an equilibrium state. The model captures some of the essential features…
Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…
We present a simple model of a vibrated box of sand, and discuss its dynamics in terms of two parameters reflecting static and dynamic disorder respectively. The fluidised, intermediate and frozen (`glassy') dynamical regimes are…
The goal of this book is to present new mathematical techniques for studying the behaviour of mean-field systems with disordered interactions. We mostly focus on certain problems of statistical inference in high dimension, and on spin…
Molecular dynamics simulations are used to generate an ensemble of saddles of the potential energy of a Lennard-Jones liquid. Classifying all extrema by their potential energy u and number of unstable directions k, a well defined relation…
Particles and fields are standard components in numerical simulations like transport simulations in nuclear physics and have very well understood dynamics. Still, a common problem is the interaction between particles and fields due to their…
The minimal cooling speed required to form a glass is obtained for a simple solvable energy landscape model. The model, made from a two-level system modified to include the topology of the energy landscape, is able to capture either a glass…
We derive the coupled non-linear integro-differential equations for the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics at temperature $T$, for spherical mixed $p$-spin disordered mean-field…
Non-equilibrium critical phenomena generally exist in many dynamic systems, like chemical reactions and some driven-dissipative {reactive} particle systems. Here, by using computer simulation and theoretical analysis, we demonstrate the…
A novel method for glassy landscape exploration is presented which utilizes a time series of energy values collected during an isothermal relaxation after a thermal quench. A sub-series of increasingly rare events, or quakes, which are…
Dynamic scaling analyses are performed in the spin-glass phase of the $\pm J$ Ising, the {\it XY}, and the Heisenberg models in three dimensions. We found a crossover from the critical dynamics to the ground-state dynamics in the Ising…