Related papers: Factorization properties in d-dimensional spin gla…
Gibbs' measures in the Sherrington-Kirkpatrick type models satisfy two asymptotic stability properties, the Aizenman-Contucci stochastic stability and the Ghirlanda-Guerra identities, which play a fundamental role in our current…
A review of the stochastic stability property for the Gaussian spin glass models is presented and some perspectives discussed.
We study the large-volume behavior of the spherical model for $d$-dimensional local spins, in the presence of $d$-dimensional random fields, for $d\geq 2$. We compare two models, one with volume-scaled random fields, and another one with…
The Ghirlanda-Guerra identities are one of the most mysterious features of spin glasses. We prove the GG identities in a large class of models that includes the Edwards-Anderson model, the random field Ising model, and the…
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 prove the property of stochastic stability previously introduced as a consequence of the (unproved) continuity hypothesis in the temperature of the spin-glass quenched state. We show that stochastic stability holds in beta-average for…
We present a general and powerful numerical method useful to study the density matrix of spin models. We apply the method to finite dimensional spin glasses, and we analyze in detail the four dimensional Edwards-Anderson model with Gaussian…
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…
Spin-glasses are natural Gibbs distributions that have been studied in Theoretical CS for many decades. Recently, they have been gaining attention from the community as they emerge naturally in neural computation and learning, network…
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…
We use a constrained Monte Carlo technique to analyze ultrametric features of a 4 dimensional Edwards-Anderson spin glass with quenched couplings J=\pm 1. We find that in the large volume limit an ultrametric structure emerges quite clearly…
We characterize numerically the properties of the phase transition of the three dimensional Ising spin glass with Gaussian couplings and of the low temperature phase. We compute critical exponents on large lattices. We study in detail the…
We show results of simulations of a weakly driven four dimensional Edwards- Anderson spin glass, which presents clear signatures of dynamical ultrametricity at low temperatures. The presence of a hierarchical organization of time scales is…
In this paper we review some recent rigorous results that provide an essentially complete solution of a class of spin glass models introduced by Derrida in the 1980ies. These models are based on Gaussian random processes on $\{-1,1\}^N$…
For Gaussian Spin Glasses in low dimensions, we introduce a simple Strong Disorder renormalization procedure at zero temperature. In each disordered sample, the difference between the ground states associated to Periodic and Anti-Periodic…
We study the four dimensional Gaussian spin glass in presence of a magnetic field. Using off-equilibrium numerical simulations we have found that the probability distribution of the overlaps is built in the same way as that of the Mean…
In this paper we study the on and off-equilibrium properties of the four dimensional Gaussian spin glass. In the static case we determine with more precision that in previous simulations both the critical temperature as well as the critical…
We present results from Monte Carlo simulations to test for ultrametricity and clustering properties in spin-glass models. By using a one-dimensional Ising spin glass with random power-law interactions where the universality class of the…
We study statistical properties of 3D classical spin glass layer of certain width and infinite length. The 3D spin glass is represented as an ensemble of disordered 1D spatial spin-chains (SSC) where interactions are random between…
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking…