Related papers: Matrix models as solvable glass models
We consider a pair of bosonic particles in a one-dimensional tight-binding periodic potential described by the Hubbard model with attractive or repulsive on-site interaction. We derive explicit analytic expressions for the two-particle…
We introduce simple models, inspired by previous models for froths and covalent glasses, with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems. These models are also a generalization of…
We introduce a class of particle models in one dimension involving exchange interactions that have scattering properties satisfying the Yang-Baxter consistency condition. A subclass of these models exhibits reflectionless scattering, in…
Tensor models are natural generalizations of matrix models. The interactions and observables in the case of unitary invariant models are generalizations of matrix traces. Some notable interactions in the literature include the melonic ones,…
We construct a matrix model equivalent (exactly, not asymptotically), to the random plane partition model, with almost arbitrary boundary conditions. Equivalently, it is also a random matrix model for a TASEP-like process with arbitrary…
The steady states of three families of one-dimensional non-equilibrium models with open boundaries, first proposed in [22], are studied using a matrix product formalism. It is shown that their associated quadratic algebras have…
We consider the dynamics of a diluted mean-field spin glass model in the aging regime. The model presents a particularly rich heterogeneous behavior. In order to catch this behavior, we perform a **spin-by-spin analysis** for a **given…
The nature of glassy dynamics and the glass transition are long-standing problems under active debate. In the presence of a structural disorder widely believed to be an essential characteristic of structural glass, identifying and…
Guided by old results on simple mode-coupling models displaying glass-glass transitions, we demonstrate, through a crude analysis of the solution with one step of replica symmetry breaking (1RSB) derived by Crisanti and Leuzzi for the…
The dynamics of strongly disordered systems becomes extremely slow or glassy at low temperatures, which results in a characteristic aging scenario. This means that the outcome of measurements strongly depends on the history of the system…
A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a…
We study the non-equilibrium relaxation of the spherical spin-glass model with p-spin interactions in the $N \rightarrow \infty$ limit. We analytically solve the asymptotics of the magnetization and the correlation and response functions…
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.…
The spherical p-spin model is not only a fundamental model in statistical mechanics of disordered system, but has recently gained popularity since many hard problems in machine learning can be mapped on it. Thus the study of the out of…
Computing the ground state of Ising spin-glass models with p-spin interactions is, in general, an NP-hard problem. In this work we show that unlike in the case of the standard Ising spin glass with two-spin interactions, computing ground…
The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the…
We study the Metropolis dynamics of a simple spin system without disorder, which exhibits glassy dynamics at low temperatures. We use an implementation of the algorithm of Bortz, Kalos and Lebowitz \cite{bortz}. This method turns out to be…
We study the non-equilibrium linear response of quantum elastic systems pinned by quenched disorder with Schwinger-Keldysh real-time techniques complemented by a mean-field variational approach. We find (i) a quasi-equilibrium regime in…
The relaxations of conductivity have been studied in the glassy regime of a strongly disordered two-dimensional electron system in Si after a temporary change of carrier density during the waiting time t_w. Two types of response have been…
The standard model of glasses is an ensemble of two-level systems interacting with a thermal bath. The general origin of memory effects in this model is a quasi-stationary but non-equilibrium state of a single two-level system, which is…