Related papers: Large random correlations in individual mean field…

The growing correlation length observed in supercooled liquids as their temperature is lowered has been studied with the aid of a single occupancy cell model. This model becomes more accurate as the density of the system is increased. One…

We introduce models of heterogeneous systems with finite connectivity defined on random graphs to capture finite-coordination effects on the low-temperature behavior of finite dimensional systems. Our models use a description in terms of…

We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as…

We present results of numerical simulations on a one-dimensional Ising spin glass with long-range interactions. Parameters of the model are chosen such that it is a proxy for a short-range spin glass above the upper critical dimension (i.e.…

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…

Multivariate spatial phenomena are ubiquitous, spanning domains such as climate, pandemics, air quality, and social economy. Cross-correlation between different quantities of interest at different locations is asymmetric in general. This…

We present a technique to generate relations connecting pure state weights, overlaps, and correlation functions in short-range spin glasses. These are obtained directly from the unperturbed Hamiltonian and hold for general coupling…

We investigate the phase structure of the random-field Ising model with a bimodal random field distribution. Our aim is to test for the possibility of an equilibrium spin-glass phase, and for replica symmetry breaking (RSB) within such a…

The gauge theory of spin glasses and statistical-mechanical formulation of error-correcting codes are reviewed with an emphasis on their similarities. For the gauge theory, we explain the functional identities on dynamical autocorrelation…

The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…

We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable…

Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorisation rules for the overlap distribution. A comparison between the state of the art for mean…

Given a countable set of sites and a collection of flip rates at each site, we give a sufficient condition on the long-range dependancies of the flip rates ensuring the well-definedness of the corresponding spin system. This hypothesis has…

Complex network theory provides an elegant and powerful framework to statistically investigate different types of systems such as society, brain or the structure of local and long-range dynamical interrelationships in the climate system.…

Long-ranged, or power-law, behavior of correlation functions in both space and time is discussed for classical systems and for quantum systems at finite temperature, and is compared with the corresponding behavior in quantum systems at zero…

We study the entanglement properties of random pure stabilizer states in spin-1/2 particles. For two contiguous groups of spins of arbitrary size we obtain a compact and exact expression for the probability distribution for the entanglement…

We discuss a phase transition in spin glass models which have been rarely considered in the past, namely the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e. at a smaller overlap) than…

We introduce a set of theoretical ideas that form the basis for an analytical framework capable of describing nonequilibrium dynamics in glassy systems. We test the resulting scenario by comparing its predictions with numerical simulations…

We study the role of fluctuations on the thermodynamic glassy properties of plaquette spin models, more specifically on the transition involving an overlap order parameter in the presence of an attractive coupling between different replicas…

It is widely accepted that the dynamic of entanglement in presence of a generic circuit can be predicted by the knowledge of the statistical properties of the entanglement spectrum. We tested this assumption by applying a Metropolis-like…