Related papers: A unified stability property in spin glasses
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…
We study numerically the structure of metastable states in the Sherrington-Kirkpatrick spin glass. We find that all non-paramagnetic stationary points of the free energy are organized into pairs, consisting in a minimum and a saddle of…
We study the quenched complexity in spin-glass mean-field models satisfying the Becchi-Rouet-Stora-Tyutin supersymmetry. The outcome of such study, consistent with recent numerical results, allows, in principle, to conjecture the absence of…
A longstanding open question in the theory of disordered systems is whether short-range models, such as the random field Ising model or the Edwards-Anderson model, can indeed have the famous properties that characterize mean-field spin…
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…
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…
We consider stochastic dynamics of lattice systems with finite local state space, possibly at low temperature, and possibly non-reversible. We assume the additional regularity properties on the dynamics: a) There is at least one stationary…
We introduce and prove a novel linear response stability theory for spin glasses. The new stability under suitable perturbation of the equilibrium state implies the whole set of structural identities that characterize the spin glass phase.
The interpolation method for mean field spin glass models developed by Guerra and Talagrand is extended to a quantum mean field spin glass model. This extension enables us to obtain both replica-symmetric (RS) and one step replica-symmetry…
Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely…
For large but finite systems the static properties of the infinite ranged Sherrington-Kirkpatrick model are numerically investigated in the entire the glass regime. The approach is based on the modified Thouless-Anderson-Palmer equations in…
We study a multi-species spin glass system where the density of each species is kept fixed at increasing volumes. The model reduces to the Sherrington-Kirkpatrick one for the single species case. The existence of the thermodynamic limit is…
If the variance of a Gaussian spin-glass Hamiltonian grows like the volume the model fulfills the Ghirlanda-Guerra identities in terms of the normalized Hamiltonian covariance.
We consider mean-field vector spin glasses with possibly non-convex interactions. Up to a small perturbation of the parameters defining the model, the asymptotic behavior of the Gibbs measure is described in terms of a critical point of an…
The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The…
Spin-glasses constitute a well-grounded framework for evolutionary models. Of particular interest for (some of) these models is the lack of self-averaging of their order parameters (e.g. the Hamming distance between the genomes of two…
In this paper we calculate the mean number of metastable states for spin glasses on so called random thin graphs with couplings taken from a symmetric binary distribution $\pm J$. Thin graphs are graphs where the local connectivity of each…
In this paper, we show that the replica symmetry of the Gibbs measure of spherical spin systems is a property of the eigenvalue spacing at the edge of the interaction matrix. In particular, our interaction matrix has \textbf{two} large…
A mean field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered. It has the same critical behavior as the Sherrington-Kirkpatrick model. It thus exhibits replica symmetry…
We study numerically a disordered model that interpolates among the Sherrington-Kirkpatrick mean field model and the three dimensional Edwards-Anderson spin glass. We find that averages over the disorder of powers of the overlap and of the…