相关论文: Cavity method in the spherical Sherrington-Kirkpat…
Let ${\boldsymbol A}\in{\mathbb R}^{n\times n}$ be a symmetric random matrix with independent and identically distributed Gaussian entries above the diagonal. We consider the problem of maximizing $\langle{\boldsymbol \sigma},{\boldsymbol…
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 generalize the strategy, we recently introduced to prove the existence of the thermodynamic limit for the Sherrington-Kirkpatrick and p-spin models, to a wider class of mean field spin glass systems, including models with multi-component…
Using a variant of the interpolating Hamiltonian technique, we show that there exists, in the Sherrington-Kirkpatrick spin glass, an exact connection between the sample-to-sample fluctuations of the free energy and bond chaos involving 2-…
A simple model of a frustrated disordered system is presented. Apart from the (very different) physical interpretation, the model shares many features with that of Sherrington-Kirkpatrick for spin glasses, but, as a consequence of its…
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…
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…
Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and…
In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging generalization of the SK model, such settings may arise…
We discuss how the kernel convolution approach can be used to accurately approximate the spatial covariance model on a sphere using spherical distances between points. A detailed derivation of the required formulas is provided. The proposed…
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…
Pion-loop corrections for Compton scattering are calculated in a novel approach based on the use of dispersion relations in a formalism obeying unitarity. The basic framework is presented, including an application to Compton scattering. In…
The mean field theory of a spin glass with a specific form of nearest and next nearest neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we either find the continuous replica symmetry breaking…
We develop analytical and numerical methods for the matrix thermofield in the large $N$ limit. Through the double collective representation on the Schwinger-Keldysh contour, it provides thermodynamical properties and finite temperature…
This paper investigates the inverse scattering problems using sampling methods with near field measurements. The near field measurements appear in two classical inverse scattering problems: the inverse scattering for obstacles and the…
We derive analytical results for the large-time relaxation of the Sherrington - Kirkpatrick model in the thermodynamic limit, starting from a random configuration. The system never achieves local equilibrium in any fixed sector of…
We study finite-size corrections to the free energy of the Sherrington-Kirkpatrick spin glass in the low temperature phase. We investigate the role of longitudinal fluctuations in these corrections, neglecting the transverse contribution.…
We present a non-perturbative Hamiltonian mapping method for quantum systems strongly coupled to a quantized field mode (cavity), yielding compact closed-form representations of hybrid light-matter systems. The mapping method builds on an…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
We propose a generalization of the cavity method to quantum spin glasses on fixed connectivity lattices. Our work is motivated by the recent refinements of the classical technique and its potential application to quantum computational…