Journal ArticleDOI
The eigenvalue spectrum of a large symmetric random matrix
Sam F. Edwards,R C Jones +1 more
TLDR
In this article, a Gaussian probability density function with the same mean and variance is used to calculate the eigenvalue spectrum of a large symmetric square matrix, each of whose upper triangular elements is described by the Gaussian distribution.Abstract:
A new and straightforward method is presented for calculating the eigenvalue spectrum of a large symmetric square matrix each of whose upper triangular elements is described by a Gaussian probability density function with the same mean and variance. Using the n to 0 method, the authors derive the semicircular eigenvalue spectrum when the mean of each element is zero and show that there is a critical finite mean value above which a single eigenvalue splits off from the semicircular continuum of eigenvalues.read more
Citations
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Journal ArticleDOI
Spin glasses: Experimental facts, theoretical concepts, and open questions
Kurt Binder,A. P. Young +1 more
TL;DR: In this article, the most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned, and a review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data.
Journal ArticleDOI
Infinite-ranged models of spin-glasses
TL;DR: In this paper, an infinite-ranged random model Hamiltonian is defined as a limiting case in which the appropriate form of mean-field theory, order parameters and phase diagram to describe spin-glasses may be established.
Proceedings ArticleDOI
Methodologies in spectral analysis of large dimensional random matrices, a review
TL;DR: In this article, a brief review of the theory of spectral analysis of large dimensional random matrices is given, including the results for the complex case of the real case, which are also of interest for researchers in electrical and electronic engineering.
Journal ArticleDOI
The statistical-mechanics of learning a rule
TL;DR: In this article, a summary of the statistical mechanical theory of learning a rule with a neural network, a rapidly advancing area which is closely related to other inverse problems frequently encountered by physicists, is presented.
Journal ArticleDOI
Cleaning large correlation matrices: Tools from Random Matrix Theory
TL;DR: This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory and establishes empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods.
References
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Journal ArticleDOI
Solvable Model of a Spin-Glass
TL;DR: In this article, an Ising model in which the spins are coupled by infinite-ranged random interactions independently distributed with a Gaussian probability density is considered and the competition between the phases and the type of order present in each is studied.
Journal ArticleDOI
Theory of spin glasses
Sam F. Edwards,Peter J. Anderson +1 more
TL;DR: In this paper, a new theory of spin glasses is proposed, which offers a simple explanation of the cusp found experimentally in the susceptibility, which is smoothed by an external field.
Journal ArticleDOI
The Spherical Model of a Ferromagnet
Theodore Berlin,Mark Kac +1 more
TL;DR: In this paper, a mathematical model of a ferromagnetic lattice is described and the limiting free energy appears in a form which contains two of the essential features of the exactly known Ising model results in one and two dimensions.
Journal ArticleDOI
Spherical Model of a Spin-Glass
TL;DR: In this article, a spin model of a spin glass is solved in the limit of infinite-ranged interactions with a gaussian probability distribution, and it is shown that for suitable values of the mean and variance of the distribution, the model can display either spin glass or ferromagnetic ordering.
Journal ArticleDOI
Theory of an impurity state in a crystal
TL;DR: A review of the theory of the effects of single-, or low-concentration impurities on the properties of otherwise perfect crystals is given in this article, where the conditions for the occurrence of localized and virtual states are discussed.