Related papers: Tailoring the overlap distribution in driven mean-…

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…

We study the creation and distribution of entanglement in disordered $XY$-type spin-$1/2$ chains for the paradigmatic case of a single flipped spin prepared on a fully polarized background. The local magnetic field is set to follow a…

Random Overlap Structures (ROSt's) are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by an isometry. In spin glasses, they arise as natural limits…

We consider a general class of disordered mean-field models where both the spin variables and disorder variables take finitely many values. To investigate the size-dependence in the phase-transition regime we construct the metastate…

I consider the problem of deriving couplings of a statistical model from measured correlations, a task which generalizes the well-known inverse Ising problem. After reminding that such problem can be mapped on the one of expressing the…

We present a numerical method to generate explicit realizations of the tree of states in mean-field spin glasses. The resulting study illuminates the physical meaning of the full replica symmetry breaking solution and provides detailed…

We study the effect of introducing separable quenched disorder on a non-equilibrium mean-field spin model exhibiting a phase transition to an oscillating state in the absence of disorder, due to non-reciprocal interactions. In the…

Spin-glass (SG) is a fascinating system that has garnered significant attention due to its intriguing properties and implications for various research fields. One of the key characteristics of spin glasses is that they contain random…

Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…

We present a large-scale simulation of the three-dimensional Ising spin glass with Gaussian disorder to low temperatures and large sizes using optimized population annealing Monte Carlo. Our primary focus is investigating the number of pure…

A random vector whose norm and overlap (inner product with an independent copy) concentrates is shown to have random low-dimensional projections that are approximately random Gaussians. Conversely, asymptotically random Gaussian projections…

We discuss the problem of ultrametricity in mean field spin glasses by means of a hierarchical clustering algorithm. We complement the clustering approach with quantitative testing: we discuss both in some detail. We show that the…

We study the large-volume behavior of the spherical model for $d$-dimensional local spins, in the presence of $d$-dimensional random fields, for $d\geq 2$. We compare two models, one with volume-scaled random fields, and another one with…

In this paper we demonstrate that two common problems in Machine Learning---imbalanced and overlapping data distributions---do not have independent effects on the performance of SVM classifiers. This result is notable since it shows that a…

We introduce the concept of Random Multi-Overlap Structures in diluted spin glasses, following the ideas of Aizenman, Sims and Starr for non-diluted models. As a result, we prove the generalized bound and variational principle for the free…

We consider models of Bayesian inference of signals with vectorial components of finite dimensionality. We show that, under a proper perturbation, these models are replica symmetric in the sense that the overlap matrix concentrates. The…

We study crosscap states in integrable field theories and spin chains in 1+1 dimensions. We derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. We then…

The main result in this paper is motivated by the M\'ezard-Parisi ansatz which predicts a very special structure for the distribution of spins in diluted mean field spin glass models, such as the random K-sat model. Using the fact that one…

Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can…

Diverse equilibrium systems with heterogeneous interactions lie at the edge of stability. Such marginally stable states are dynamically selected as the most abundant ones or as those with the largest basins of attraction. On the other hand,…