Related papers: On the self-overlap in vector spin glasses
Spin glasses are quintessential examples of complex matter. Although much about their order remains uncertain, abstract models of them inform, e.g., the classification of combinatorial optimization problems, the magnetic ordering in metals…
Perfect lensing using negative refractive index materials and radiationless electromagnetic interference both provide extreme subwavelength focusing by "amplifying" evanescent wave components that are usually lost. This paper provides a…
The full replica symmetry breaking free energy of the Ising spin glass on random regular graphs is given by the solutions of two auxiliary variational problems inside a global (physical) variational problem on the order parameter. In this…
We study the free energy for pure and mixed spherical $p$-spin models with i.i.d.\ disorder. In the mixed case, each $p$-interaction layer is assumed either to have regularly varying tails with exponent $\alpha_p$ or to satisfy a finite…
In these notes, we continue our investigation of classical toy models of disordered statistical mechanics through various techniques recently developed and tested mainly on the paradigmatic SK spin glass. Here we consider the p-spin-glass…
We compute numerically small window overlaps in the three dimensional Edwards Anderson spin glass. We show that they behave in the way implied by the Replica Symmetry Breaking Ansatz, that they do not qualitatively differ from the full…
We discuss a generalization of the conditions of validity of the interpolation method for the density of quenched free energy of mean field spin glasses. The condition is written just in terms of the $L^2$ metric structure of the Gaussian…
We show that, above the critical temperature, if the dimension D of a given Ising spin glass model is sufficiently high, its free energy can be effectively expressed through the free energy of a related Ising model. When, in a large sense,…
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…
In this short note, we consider models of optimal Bayesian inference of finite-rank tensor products. We add to the model a linear channel parametrized by $h$. We show that at every interior differentiable point $h$ of the free energy…
There is a rich history of expressing the limiting free energy of mean-field spin glasses as a variational formula over probability measures on $[0,1]$, where the measure represents the similarity (or "overlap") of two independently sampled…
We prove a central limit theorem for the normalized overlap between two replicas in the spherical SK model in the high temperature phase. The convergence holds almost surely with respect to the disorder variables, and the inverse…
We consider the behavior of the overlap of $m (\geq 2)$ paths at the spin glass transition for a directed polymer in a random medium. We show that an infinite number of exponents is required to describe these overlaps. This is done in an…
The nature of equilibrium states in disordered materials is often studied using an overlap function P(q), the probability of two configurations having similarity q. Exact sampling simulations of a two-dimensional proxy for three-dimensional…
We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, Stochastic…
In recent years scale invariant scattering theory provided the first exact access to the magnetic critical properties of two-dimensional statistical systems with quenched disorder. We show how the theory extends to the overlap variables…
We describe the large deviations above its typical value of the maximal energy of a spin glass with +/-1 spins. Thanks to the relatively explicit description of the rate function we identify, we then show that the latter is asymptotically…
For random combinatorial optimization problems, there has been much progress in establishing laws of large numbers and computing limiting constants for the optimal value of various problems. However, there has not been as much success in…
We show through a simple example that perturbations of the Hamiltonian of a spin glass which cannot be detected at the level of the free energy can completely alter the behavior of the overlap. In particular, perturbations of order O(log…
We perform large scale simulations of the frustrated Ising lattice gas, a three-dimensional lattice model of a structural glass, using the parallel tempering technique. We evaluate the spin and density overlap distributions, and the…