Related papers: Optimizing Mean Field Spin Glasses with External F…
We study the phenomenon of the locking of the order parameter (or synchronization) in spin glasses at low temperatures. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this…
We use the generic replica symmetric cubic field-theory to study the transition of short range Ising spin glasses in a magnetic field around the upper critical dimension, d=6. A novel fixed-point is found, in addition to the well-known zero…
In this paper I will describe some results that have been recently obtained in the study of random Euclidean matrices, i.e. matrices that are functions of random points in Euclidean space. In the case of {\sl translation invariant} matrices…
We study the high-temperature regime of a mean-field spin glass model whose couplings matrix is orthogonally invariant in law. The magnetization of this model is conjectured to satisfy a system of TAP equations, originally derived by Parisi…
Generative models have been successfully used for generating realistic signals. Because the likelihood function is typically intractable in most of these models, the common practice is to use "implicit" models that avoid likelihood…
Numerical studies in random systems are plagued with strong finite-size effects and boundary effects. We introduce a window-measurement method as a practical solution to these difficulties. We observe physical quantities only within a…
The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two…
We establish the local asymptotic normality (LAN) property for estimating a multidimensional parameter in the drift of a system of $N$ interacting particles observed over a fixed time horizon in a mean-field regime $N \rightarrow \infty$.…
We design a deterministic algorithm that, given $n$ points in a \emph{typical} constant degree regular~graph, queries $O(n)$ distances to output a constant factor approximation to the average distance among those points, thus answering a…
By using renormalization-group (RG) methods, we study a non-mean-field model of a spin glass built on a hierarchical lattice, the hierarchical Edwards-Anderson model in a magnetic field. We investigate the spin-glass transition in a field…
In the present paper we analyze the critical properties of a quantum spherical spin glass model with short range, random interactions. Since the model allows for rigorous detailed calculations, we can show how the effective partition…
The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard `mean-field theory' versus `droplet picture' debate of the last decades. The main predictions of both theories…
In this talk we present the exact solution of the most general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbour interactions, and we discuss the possible continuum limits. All these…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
We study the role of Hamiltonian complexity in the performance of quantum annealers. We consider two general classes of annealing Hamiltonians: stoquastic ones, which can be simulated efficiently using the quantum Monte Carlo algorithm, and…
The classical transverse field Ising spin- glass model with short-range interactions is investigated beyond the mean- field approximation for a real d- dimensional lattice. We use an appropriate nontrivial modification of the Bethe- Peierls…
We describe two quantum algorithms to approximate the mean value of a black-box function. The first algorithm is novel and asymptotically optimal while the second is a variation on an earlier algorithm due to Aharonov. Both algorithms have…
We investigate the relationship between algorithmic fractal dimensions and the classical local fractal dimensions of outer measures in Euclidean spaces. We introduce global and local optimality conditions for lower semicomputable outer…
We develop a systematic expansion method of physical quantities for the SK model and the finite-dimensional $\pm J$ model of spin glasses in non-equilibrium states. The dynamical probability distribution function is derived from the master…
A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that…