Related papers: About the cavity fields in mean field spin glass m…

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…

The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics the same way the random energy model clarifies spin glass behavior would…

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…

We study the geometrical structure of the states in the low temperature phase of a mean field model for generalized spin glasses, the p-spin spherical model. This structure cannot be revealed by the standard methods, mainly due to the…

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…

We have combined the dynamical mean field theories of the Mott transition and the spin glass in infinite dimensions and derived a metallic spin-glass state from a random spin-fermion model.

In this paper we study the fluctuations of the probability distributions of the overlap in mean field spin glasses in the presence of a magnetic field on the De Almeida-Thouless line. We find that there is a large tail in the left part of…

For the discrete random field Curie-Weiss models, the infinite volume Gibbs states and metastates have been investigated and determined for specific instances of random external fields. In general, there are not many examples in the…

The spontaneous supersymmetry-breaking that takes place in certain spin-glass models signals a particular fragility in the structure of metastable states of such systems. This fragility is due to the presence of at least one marginal mode…

The introduction of ``small permutations'' allows us to derive Ward-Takahashi identities for the spin-glass, in the Parisi limit of an infinite number of steps of replica symmetry breaking. The first identities express the emergence of a…

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…

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…

In this work we give a proof of universality with respect to the choice of the statistical distribution of the quenched noise, for mean field bipartite spin glasses. We use mainly techniques of spin glasses theory, as Guerra's interpolation…

We propose a method for calculating the Franz-Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the…

A disordered mean field model for multimode laser in open and irregular cavities is proposed and discussed within the replica analysis. The model includes the dynamics of the mode intensity and accounts also for the possible presence of a…

The Sherrington-Kirkpatrick spin-glass model is investigated by means of Monte Carlo simulations employing a combination of the multi-overlap algorithm with parallel tempering methods. We investigate the finite-size scaling behaviour of the…

This thesis focus on the extension of the Parisi full replica symmetry breaking solution to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-M\'ezard cavity…

For a very general class of probability distributions in disordered Ising spin systems, in the thermodynamical limit, we prove the following property for overlaps among real replicas. Consider the overlaps among s replicas. Add one replica…

Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…

We present results of recent high-statistics Monte Carlo simulations of the Edwards-Anderson Ising spin-glass model in three and four dimensions. The study is based on a non-Boltzmann sampling technique, the multi-overlap algorithm which is…