相关论文: Real space application of the mean-field descripti…
We introduce a diluted version of the one dimensional spin-glass model with interactions decaying in probability as an inverse power of the distance. In this model varying the power corresponds to change the dimension in short-range models.…
We review the main methods used to study spin glasses. In the first part, we focus on methods for fully connected models and systems defined on a tree, such as the replica method, the Thouless-Anderson-Palmer formalism, the cavity method,…
We analyze numerically the violation of the fluctuation-dissipation theorem (FDT) in the $\pm J$ Edwards-Anderson (EA) spin glass model. Using single spin probability densities we reveal the presence of strong dynamical heterogeneities,…
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…
In an effort to understand the glass transition, the kinetics of a spin model with frustration but no quenched randomness has been analyzed. The phenomenology of the spin model is remarkably similiar to that of structural glasses. Analysis…
Mean-field theories of the glass transition predict a phase transition to a dynamically arrested state, yet no such transition is observed in experiments or simulations of finite-dimensional systems. We resolve this long-standing…
We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in…
The analytical solution to the out-of-equilibrium dynamics of mean-field spin glasses has profoundly shaped our understanding of glassy dynamics, which take place in many diverse physical systems. In particular, the idea that during the…
As in the preceding paper we aim at identifying the effective theory that describes the fluctuations of the local overlap with an equilibrium reference configuration close to a putative thermodynamic glass transition. We focus here on the…
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…
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…
We study the violation of the fluctuation-dissipation theorem in the three and four dimensional Gaussian Ising spin glasses using on and off equilibrium simulations. We have characterized numerically the function X(C) that determine the…
We consider the stationary state of a fluid comprised of inelastic hard spheres or disks under the influence of a random, momentum-conserving external force. Starting from the microscopic description of the dynamics, we derive a nonlinear…
Motivated by the mean field prediction of a Gardner phase transition between a "normal glass" and a "marginally stable glass", we investigate the off-equilibrium dynamics of three-dimensional polydisperse hard spheres, used as a model for…
The statics-dynamics correspondence in spin glasses relate non-equilibrium results on large samples (the experimental realm) with equilibrium quantities computed on small systems (the typical arena for theoretical computations). Here we…
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…
Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…
Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-field theories of spin models on networks constitute a…
Spin glass dynamics is a strong function of spatial dimensionality $D$. The lower critical dimension is close to 2.5, so that, in two dimensions, the condensation temperature $T_\text{g}=0$, and only fluctuations are present at finite…
We unveil the multifractal behavior of Ising spin glasses in their low-temperature phase. Using the Janus II custom-built supercomputer, the spin-glass correlation function is studied locally. Dramatic fluctuations are found when pairs of…