Related papers: Beyond the Sherrington-Kirkpatrick Model
connected spin-glass models with a discontinuous transition. In the thermodynamic limit the equilibrium properties in the high temperature phase are described by the schematic Mode Coupling Theory of super-cooled liquids. We show that {\it…
In this paper and in the companion one we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems---the overlap field…
A construction supporting a conjecture that different ground state pairs exist in the 2-dimensional Edwards-Anderson Ising spin glass is presented.
This study focuses on the problem of finding ground states of random instances of the Sherrington-Kirkpatrick (SK) spin-glass model with Gaussian couplings. While the ground states of SK spin-glass instances can be obtained with branch and…
We study spin glasses with Kac type interaction potential for small but finite inverse interaction range $\gamma$. Using the theoretical setup of coupled replicas, through the replica method we argue that the probability of overlap profiles…
Typical features of glass phenomenology such as the Vogel-Fulcher law, the Kauzmann paradox and the Adam-Gibbs relationship are shown to follow from the recently discovered mapping of glasses to Ising spin glasses in a magnetic field. There…
We review main features and problems of higher spin field theory and flash some ways along which it has been developed over last decades.
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…
This is a reply to cond-mat/0010033 by Newman and Stein, which is a comment on on our paper Phys. Rev. Lett. 85, 3017 (2000), cond-mat/0002134.
We provide rigorous proofs which show that the main features of the Parisi solution of the Sherrington-Kirkpatrick spin glass are not valid for more realistic spin glass models in any dimension and at any temperature.
Using a stochastic algorithm introduced in a previous paper, we study the finite size volume corrections and the fluctuations of the ground state energy in the Sherrington-Kirkpatrick and the Edwards-Anderson models at zero temperature. The…
We consider a multi-layer Sherrington-Kirkpatrick spin-glass as a model for deep restricted Boltzmann machines and we solve for its quenched free energy, in the thermodynamic limit and allowing for a first step of replica symmetry breaking.…
In connection with recent discussion of topological order and topological phase transitions in quantum systems, we reexamine circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local…
We study numerically the three-dimensional $\phi^{4}$ spin glass, a prototypical disordered and discretized Euclidean field theory that manifests inhomogeneities in space and time but considers a homogeneous squared mass and lambda terms.…
Spin glasses are the paradigm of complex systems. These materials present really slow dynamics. However, the nature of the spin glass phase in finite dimensional systems is still controversial. Different theories describing the low…
The aim of this review paper is to give a panoramic of the impact of spin glass theory and statistical physics in the study of the K-sat problem. The introduction of spin glass theory in the study of the random K-sat problem has indeed left…
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…
We provide here a brief perspective on the glass transition field. It is an assessment, written from the point of view of theory, of where the field is and where it seems to be heading. We first give an overview of the main phenomenological…
I present a new method to analyze Glauber dynamics of the Sherrington-Kirkpatrick (SK) spin glass model. The method is based on ideas used in the classical kinetic theory of fluids. I apply it to study spin correlations in the high…
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…