Related papers: On Spin-Glass Complexity
We study the equilibrium properties of an Ising frustrated lattice gas with a mean field replica approach. This model bridges usual {\em Spin Glasses} and a version of {\em Frustrated Percolation} model, and has proven relevant to describe…
In this paper a multi-scale version of the Sherrington and Kirkpatrick model is introduced and studied. The pressure per particle in the thermodynamical limit is proved to obey a variational principle of Parisi type. The result is achieved…
A recent interesting paper [Yucesoy et al. Phys. Rev. Lett. 109, 177204 (2012), arXiv:1206:0783] compares the low-temperature phase of the 3D Edwards-Anderson (EA) model to its mean-field counterpart, the Sherrington-Kirkpatrick (SK) model.…
We discuss interfaces in spin glasses. We present new theoretical results and a numerical method to characterize overlap interfaces and the stability of the spin-glass phase in extended disordered systems. We use this definition to…
The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The…
The Sherrington--Kirkpatrick model of spin glasses, the Hopfield model of neural networks and the Ising spin glass are all models of binary data belonging to the one-parameter exponential family with quadratic sufficient statistic. Under…
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…
In this paper, we show that the replica symmetry of the Gibbs measure of spherical spin systems is a property of the eigenvalue spacing at the edge of the interaction matrix. In particular, our interaction matrix has \textbf{two} large…
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…
In this paper we consider central limit theorems for various macroscopic observables in the high temperature region of the Sherrington-Kirkpatrick spin glass model. With a particular focus on obtaining a quenched central limit theorem for…
In many spin glass models, due to the symmetry among sites, any limiting joint distribution of spins under the annealed Gibbs measure admits the Aldous-Hoover representation encoded by a function $\sigma:[0,1]^4\to\{-1,+1\}$, and one can…
In certain mean field models for spin glasses there occurs a one step replica symmetry breaking pattern. As an example of general $1/N$-corrections in such systems, the fluctuations in the internal energy are calculated. For this specific…
We study properties of the energy minima obtained by quenching equilibrium configurations of the Sherrington-Kirkpatrick (SK) mean field spin glass. We measure the probability distribution of the overlap among quenched configurations and…
In these short notes, we adapt and systematically apply Guerra's interpolation techniques on a class of disordered mean-field spin glasses equipped with crystal fields and multi-value spin variables. These models undergo the phenomenon of…
Spin glasses are quintessential examples of complex matter. Although much about their order remains uncertain, abstract models of them inform, e.g., the classification of combinatorial optimization problems, the magnetic ordering in metals…
We examine the behavior of the 2-spin spherical Sherrington-Kirkpatrick model with an external field by analyzing the overlap of a spin with the external field. Previous research has noted that, at low temperature, this overlap exhibits…
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…
Disordered systems generically exhibit aging and a glass transition. Previous studies have long suggested that non-reciprocity tends to destroy glassiness. Here, we show that this is not always the case using a bipartite spherical…
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…
Critical slowing down dynamics of supercooled glass-forming liquids is usually understood at the mean-field level in the framework of Mode Coupling Theory, providing a two-time relaxation scenario and power-law behaviors of the time…