Related papers: Spin glass polynomial identities from entropic con…

We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of…

Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…

The present paper proposes a Statistical Mechanics approach to the inherent states of glassy systems and granular materials, following the original ideas developed by Edwards for granular materials. Two lattice models, a diluted Spin Glass…

In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…

Aim of this paper is to give an extensive treatment of bipartite mean field spin systems, ordered and disordered: at first, bipartite ferromagnets are investigated, achieving an explicit expression for the free energy trough a new minimax…

We investigate scenarios in which the low-temperature phase of short-range spin glasses comprises thermodynamic states which are nontrivial mixtures of multiple incongruent pure state pairs. We construct a new kind of metastate supported on…

In this short note we study the fourth order consequences of the stochastic stability property for mean field spin glass models introduced in previous paper by Aizenman and Contucci. We show that due to a remarkable cancellation mechanism…

Entropic independence is a structural property of measures that underlies modern proofs of functional inequalities, notably (modified) log-Sobolev inequalities, via ``annealing'' or local-to-global schemes. Existing sufficient criteria for…

We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…

We study the properties of fluctuation for the free energies and internal energies of two spin glass systems that differ for having some set of interactions flipped. We show that their difference has a variance that grows like the volume of…

We introduce a diagrammatic formulation for a cavity field expansion around the critical temperature. This approach allows us to obtain a theory for the overlap's fluctuations and, in particular, the linear part of the Ghirlanda-Guerra…

The theory of integral quadratic constraints (IQCs) allows verification of stability and gain-bound properties of systems containing nonlinear or uncertain elements. Gain bounds often imply exponential stability, but it can be challenging…

Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While stress-strain curves for a wide range of temperature can be fit to the functional form predicted by entropic network models, many other…

This paper deals with the stochastic Ising model with a temperature shrinking to zero as time goes to infinity. A generalization of the Glauber dynamics is considered, on the basis of the existence of simultaneous flips of some spins. Such…

The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally…

The statics-dynamics correspondence in spin glasses relate non-equilibrium results on large samples (the experimental realm) with equilibrium quantities computed on small systems (the typical arena for theoretical computations). Here we…

The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with highly diversified collections of competing low energy states. The goal of this summary is to present some…

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…

A spin-glass transition occurs both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance.…

We study the stochastic relaxation dynamics of the Ising p-spin model on a random graph, a well-known model with glassy dynamics at low temperatures. We introduce and discuss a new closure scheme for the master equation governing the…