相关论文: Fluctuations of the overlap at low temperature in …

We investigate the fluctuations of the free energy of the $2$-spin spherical Sherrington-Kirkpatrick model at critical temperature $\beta_c = 1$. When $\beta = 1$ we find asymptotic Gaussian fluctuations with variance $\frac{1}{6N^2}…

We prove a central limit theorem for the normalized overlap between two replicas in the spherical SK model in the high temperature phase. The convergence holds almost surely with respect to the disorder variables, and the inverse…

In a region above the Almeida-Thouless line, where we are able to control the thermodynamic limit of the Sherrington-Kirkpatrick model and to prove replica symmetry, we show that the fluctuations of the overlaps and of the free energy are…

We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, Stochastic…

In order to study certain questions concerning the distribution of the overlap in Sherrington--Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the free energy of multiple systems with…

Based on \cite{H}, it is well known that the rescaled two point correlation functions \[ \sqrt{N} \langle \sigma_i ; \sigma_j\rangle = \sqrt{N} \big( \langle \sigma_i \sigma_j\rangle -\langle \sigma_i\rangle \langle \sigma_j\rangle\big) \]…

The spherical Sherrington-Kirkpatrick model is a spherical mean field model for spin glass. We consider the fluctuations of the free energy at arbitrary non-critical temperature for the 2-spin model with no magnetic field. We show that in…

We analyze the fluctuations of the free energy, replica overlaps, and overlap with the external field in the quadratic spherical SK model with a magnetic field. We identify several different behaviors for these quantities depending on the…

We prove the convergence in distribution of the fluctuations of the free energy of the mixed $p$-spin Sherrington-Kirkpatrick model with non-vanishing $2$-spin component at high enough temperature. The limit is Gaussian, and the…

We compute the fluctuations of the magnetization and of the multi-overlaps for the dilute mean field ferromagnet, in the high temperature region. The rescaled magnetization tends to a centered Gaussian variable with variance diverging at…

We explore the joint behavior of a finite number of multi-overlaps in the high temperature phase of the SK model. Extending work by M. Talagrand, we show that, when these objects are scaled to have non-trivial limiting distributions, the…

We consider the random fluctuations of the free energy in the $p$-spin version of the Sherrington-Kirkpatrick model in the high temperature regime. Using the martingale approach of Comets and Neveu as used in the standard SK model combined…

We consider a spherical spin system with pure 2-spin spherical Sherrington-Kirkpatrick Hamiltonian with ferromagnetic Curie-Weiss interaction. The system shows a two-dimensional phase transition with respect to the temperature and the…

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…

We obtain an exact analytic expression for the average distribution, in the thermodynamic limit, of overlaps between two copies of the same random energy model (REM) at different temperatures. We quantify the non-self averaging effects and…

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 study here the random fluctuations in the number of critical points with values in an interval $I\subset \mathbb{R}$ for Gaussian spherical eigenfunctions $\left\{f_{\ell }\right\} $, in the high energy regime where $\ell \rightarrow…

Covariances and variances of linear statistics of a point process can be written as integrals over the truncated two-point correlation function. When the point process consists of the eigenvalues of a random matrix ensemble, there are often…

The spin glass behavior near zero temperature is a complicated matter. To get an easier access to the spin glass order parameter $Q(x)$ and, at the same time, keep track of $Q_{ab}$, its matrix aspect, and hence of the Hessian controlling…

We consider the statistical properties over disordered samples of the overlap distribution $P_{\cal J}(q)$ which plays the role of an order parameter in spin-glasses. We show that near zero temperature (i) the {\it typical} overlap…