Related papers: Random Overlap Structures: Properties and Applicat…
Properties of Random Overlap Structures (ROSt)'s constructed from the Edwards-Anderson (EA) Spin Glass model on $\Z^d$ with periodic boundary conditions are studied. ROSt's are $\N\times\N$ random matrices whose entries are the overlaps of…
A random overlap structure (ROSt) is a measure on pairs (X,Q) where X is a locally finite sequence in the real line with a maximum and Q a positive semidefinite matrix of overlaps intrinsic to the particles X. Such a measure is said to be…
We investigate overlap fluctuations of the Sherrington-Kirkpatrick mean field spin glass model in the framework of the Random Over- lap Structure (ROSt). The concept of ROSt has been introduced recently by Aizenman and coworkers, who…
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 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…
In these notes we review first in some detail the concept of random overlap structure (ROSt) applied to fully connected and diluted spin glasses. We then sketch how to write down the general term of the expansion of the energy part from the…
In this note, we point out that infinite-volume Gibbs measures of spin glass models on the hypercube can be identified as random probability measures on the unit ball of a Hilbert space. This simple observation follows from a result of…
Spin-glass theory is one of the leading paradigms of complex physics and describes condensed matter, neural networks and biological systems, ultracold atoms, random photonics, and many other research fields. According to this theory,…
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 prove that the Aizenman-Contucci relations, well known for fully connected spin glasses, hold in diluted spin glasses as well. We also prove more general constraints in the same spirit for multi-overlaps, systematically confirming and…
We present a combination of heuristic and rigorous arguments indicating that both the pure state structure and the overlap structure of realistic spin glasses should be relatively simple: in a large finite volume with coupling-independent…
We continue our presentation of mathematically rigorous results about the Sherrington-Kirkpatrick mean field spin glass model. Here we establish some properties of the distribution of overlaps between real replicas. They are in full…
In this paper we prove that the support of a random measure on the unit ball of a separable Hilbert space that satisfies the Ghirlanda-Guerra identities must be ultrametric with probability one. This implies the Parisi ultrametricity…
The behavior of a newly introduced overlap parameter is analyzed, measuring the correlation between intensity fluctuations of waves in random media in different physical regimes, with varying amount of disorder and non-linearity. Its…
We give the explicit expression of the infinite volume limit for the random overlap structures appearing in the mean field spin glass model. These structures have the expected factorization property for the cavity fields, and enjoy…
During the last years, through the combined effort of the insight, coming from physical intuition and computer simulation, and the exploitation of rigorous mathematical methods, the main features of the mean field Sherrington-Kirkpatrick…
The mean field spin glass model is analyzed by a combination of mathematically rigororous methods and a powerful Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural…
We discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibrium, the limit value of the free energy at long times is equal to the equilibrium free…
We study the chaotic behavior of the Gibbs state of spin-glasses under the application of an external magnetic field, in the crossover region where the field intensity scales proportional to $1/\sqrt{N}$, being $N$ the system size. We show…
The Ghatak-Sherrington (GS) spin glass model is a random probability measure defined on the configuration space $\{0,\pm1,\pm2,\ldots, \pm \mathcal{S} \}^N$ with system size $N$ and $\mathcal{S}\ge1$ finite. This generalizes the classical…