Related papers: Spin Glass Model of Operational Risk

We introduce a lattice spin model where frustration is due to multibody interactions rather than quenched disorder in the Hamiltonian. The system has a crystalline ground state and below the melting temperature displays a dynamic behaviour…

We study the low temperature dynamics of a two dimensional short-range spin system with uniform ferromagnetic interactions, which displays glassiness at low temperatures despite the absence of disorder or frustration. The model has a dual…

In these lectures I will review some theoretical results that have been obtained for spin glasses. I will concentrate my attention on the formulation of the mean field approach and on its numerical and experimental verifications. I will…

This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…

We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…

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,…

Most of the analytical studies on spin glasses are performed by using mean-field theory and renormalization group analysis. Analytical studies on finite-dimensional spin glasses are very challenging. In this short note, a possible exten-…

Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental…

We review recent theoretical progress on glassy dynamics, with special emphasis on the importance and universality of the ``aging regime'', which is relevant to many experimental situations. The three main subjects which we address are: (i)…

This lecture deals with glassy dynamics and aging in disordered systems. Special emphasis is put on dynamic mean field theory. In the first part I present some of the systems of interest, in particular spin-glasses, supercooled liquids and…

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 discuss the status of Monte Carlo simulations of (mainly finite dimensional) spin glass systems. After a short historical note and a brief theoretical introduction we start by discussing the (crucial) 3D case: the warm phase, the…

A disordered spin model suitable for studying inverse freezing in fragile glass-forming systems is introduced. The model is a microscopic realization of the ``random-first order'' scenario in which the glass transition can be either…

We study the role of different terms in the $N$-body potential of glass forming systems on the critical dynamics near the glass transition. Using a simplified spin model with quenched disorder, where the different terms of the real $N$-body…

Systematic and multifactor risk models are revisited via methods which were already successfully developed in signal processing and in automatic control. The results, which bypass the usual criticisms on those risk modeling, are illustrated…

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…

We revisit the concept of marginal stability in glasses, and determine its range of applicability in the context of avalanche-type response to slow external driving. We argue that there is an intimate connection between a pseudo-gap in the…

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…

Within the wide class of disordered materials, spin glasses occupy a special place because of their conceptually simple definition of randomly interacting spins. Their modelling has triggered spectacular developments of out-of-equilibrium…

Spin Glasses (SG) are paradigmatic models for physical, computer science, biological and social systems. The problem of studying the dynamics for SG models is NP hard, i.e., no algorithm solves it in polynomial time. Here we implement the…