Related papers: Solving the fully-connected spherical $p$-spin mod…
We discuss the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry…
A continuous 3-state Potts model with an analog of spherical constraints is proposed and is shown to have an exact solution in the case of infinite-ranged interactions. "Spherical" 3-state Potts spin glass model is solved using the known…
An one-step replica-symmetry-breaking solution for finite connectivity spin-glass models with K body interaction is constructed at finite temperature using the replica method and thermodynamic constraints. In the absence of external fields,…
We prove a Parisi formula for the limiting free energy of multi-species spherical spin glasses with mixed $p$-spin interactions. The upper bound involves a Guerra-style interpolation and requires a convexity assumption on the model's…
The cavity method is a well established technique for solving classical spin models on sparse random graphs (mean-field models with finite connectivity). Laumann et al. [arXiv:0706.4391] proposed recently an extension of this method to…
We present a method for general relativistic smoothed particle hydrodynamics (GRSPH), based on an entropy-conservative form of the general relativistic hydrodynamic equations for a perfect fluid. We aim to replace approximate treatments of…
Infinite-range spin-glass models with Levy-distributed interactions show a freezing transition similar to disordered spin systems on finite connectivity random graphs. It is shown that despite diverging moments of the local field…
In an array of coupled cavities where the cavities are doped with an atomic V-system, and the two excited levels couple to cavity photons of different polarizations, we show how to construct various spin models employed in characterizing…
We propose a scheme to realize the Heisenberg model of any spin in an arbitrary array of coupled cavities. Our scheme is based on a fixed number of atoms confined in each cavity and collectively applied constant laser fields, and is in a…
In a companion paper we developed the generalized TAP approach for general multi-species spherical mixed $p$-spin models. In this paper, we use it to compute the limit of the free energy at any temperature for all pure multi-species…
We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions and a global spherical constraint at zero magnetic field. The replicated spin-glass Hamiltonian is mapped onto a Coulomb gas of…
This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) have been extensively studied for solving PDEs by…
The large-system performance of MAP estimation is studied considering a general distortion function when the observation vector is received through a linear system with additive white Gaussian noise. The analysis considers the system matrix…
Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…
We study the stochastic dynamics of Ising spin models with random bonds, interacting on finitely connected Poissonnian random graphs. We use the dynamical replica method to derive closed dynamical equations for the joint spin-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…
This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems. The main tools are the graphical models and approximate message-passing algorithm together with the cavity…
Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) that becomes infeasible for shapes with high sampling density. A promising research direction is to tackle such quadratic optimization problems…
The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally…
An encryption of a signal ${\bf s}\in\mathbb{R^N}$ is a random mapping ${\bf s}\mapsto \textbf{y}=(y_1,\ldots,y_M)^T\in \mathbb{R}^M$ which can be corrupted by an additive noise. Given the Encryption Redundancy Parameter (ERP) $\mu=M/N\ge…