Related papers: Toward a Classification of Stochastically Stable Q…

The Griffiths first and second inequalities have played an important role in the analysis of ferromagnetic models. In spin-glass models, although the counterpart of the Griffiths first inequality has been obtained, the counterpart of the…

A comprehensive review will be given about the rich mathematical structure of mean field spin glass theory, mostly developed, until now, in the frame of the methods of theoretical physics, based on deep physical intuition and hints coming…

The main result in this paper is motivated by the M\'ezard-Parisi ansatz which predicts a very special structure for the distribution of spins in diluted mean field spin glass models, such as the random K-sat model. Using the fact that one…

I discuss results from numerical simulations of finite dimensional spin glass models, and show that they show all signatures of a mean field like behavior, basically coinciding with the one of the Parisi solution. I discuss the Binder…

We reply to the comment of Marinari and Parisi [cond-mat/0002457 v2] on our paper [Phys. Rev. Lett. 83, 5126 (1999) and cond-mat/9906323]. We show that the data in the comment are affected by strong finite-size corrections. Therefore the…

This is a short review about recent methods and results, mostly for mean field spin glasses, based on interpolation and comparison schemes. In particular, the Parisi spontaneous replica symmetry breaking phenomenon is described in the frame…

We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original…

We investigate the properties of the glass phase of a recently introduced spin glass model of soft spins subjected to an anharmonic quartic local potential, which serves as a model of low temperature molecular or soft glasses. We solve the…

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…

By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend…

We prove that, in mixed $p$-spin models of spin glasses, the location of the ground state is chaotic under small Gaussian perturbations. For the case of even $p$-spin models, this was shown by Chen, Handschy and Lerman [2018]. We rely on a…

Truly stable metastable states are an artifact of the mean-field approximation or the zero temperature limit. If such appealing concepts in glass theory as configurational entropy are to have a meaning beyond these approximations, one needs…

According to the droplet picture of spin glasses, the low-temperature phase of spin glasses should be replica symmetric. However, analysis of the stability of this state suggested that it was unstable and this instability lends support to…

We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the…

The Parisi solution of the mean-field spin glass has been widely accepted and celebrated. Its marginal stability in 3d and its complexity however raised the question of its relevance to real spin glasses. This paper gives a short overview…

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 consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function $q(x)$ is computed at high orders in powers of $\tau=T_c-T$ and $H$. We find that none of…

We study the stability of the replica-symmetric solution of a two-sublattice infinite-range spin-glass model, which can describe the transition from antiferromagnetic to spin glass state. The eigenvalues associated with replica-symmetric…

In talk I will review the theoretical results that have been obtained for spin glasses, paying a particular attention to finite dimensional spin glasses. I will concentrate my attention on the formulation of the mean field approach and on…

A theoretical analysis [Angelani et al., Phys. Rev. Lett. 96, 065702 (2006)] predicts glassy behaviour of light in a nonlinear random medium. This implies slow dynamics related to the presence of many metastable states. We consider very…