Related papers: Toward a Classification of Stochastically Stable Q…
While the Gibbs states of spin glass models have been noted to have an erratic dependence on temperature, one may expect the mean over the disorder to produce a continuously varying ``quenched state''. The assumption of such continuity in…
In these two lectures I review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently…
In this talk we review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently…
Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorisation rules for the overlap distribution. A comparison between the state of the art for mean…
We study the chaotic nature of spin glasses against perturbations of the realization of the quenched disorder. This type of perturbation modifies the energy landscape of the system without adding extensive energy. We exactly solve the…
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…
These lecture notes focus on the mean field theory of spin glasses, with particular emphasis on the presence of a very large number of metastable states in these systems. This phenomenon, and some of its physical consequences, will be…
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…
The core idea of stochastic stability is that thermodynamic observables must be robust under small (random) perturbations of the quenched Gibbs measure. Combining this idea with the cavity field technique, which aims to measure the free…
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 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…
A review of the stochastic stability property for the Gaussian spin glass models is presented and some perspectives discussed.
We sketch a new framework for the analysis of disordered systems, in particular mean field spin glasses, which is variational in nature and within the formalism of classical thermodynamics. For concreteness, only the Sherrington-Kirkpatrick…
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…
After introducing and discussing the "link-overlap" between spin configurations we show that the Edwards-Anderson model has a "replica-equivalent" quenched equilibrium state, a property introduced by Parisi in the description of the…
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…
We consider the p-spin spherical spin-glass model in the presence of an external magnetic field as a general example of a mean-field system where a one step replica symmetry breaking (1-RSB) occurs. In this context we compute the complexity…
We discuss the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry…
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…
Models of spin glasses are studied with a phase transition discontinuous in the Parisi order parameter. It is assumed that the leading order corrections to the thermodynamic limit of the high temperature free energy are due to the existence…