Topic

# Correlation function

About: Correlation function is a research topic. Over the lifetime, 4925 publications have been published within this topic receiving 121772 citations.

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TL;DR: Distance correlation is a new measure of dependence between random vectors that is based on certain Euclidean distances between sample elements rather than sample moments, yet has a compact representation analogous to the classical covariance and correlation.

Abstract: Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the classical covariance and correlation. Asymptotic properties and applications in testing independence are discussed. Implementation of the test and Monte Carlo results are also presented.

2,042 citations

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TL;DR: A valence-bond solid is presented, which is simply constructed out of valence bonds, is nondegenerate, and breaks no symmetries, and there is an energy gap and an exponentially decaying correlation function.

Abstract: We present rigorous results on a phase in antiferromagnets in one dimension and more, which we call a valence-bond solid. The ground state is simply constructed out of valence bonds, is nondegenerate, and breaks no symmetries. There is an energy gap and an exponentially decaying correlation function. Physical applications are mentioned.

1,550 citations

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TL;DR: The explicitly soluble Luttinger model is used as a basis for the description of the general interacting Fermi gas in one dimension, which will be called "LUTtinger liquid theory" as mentioned in this paper.

Abstract: The explicitly soluble Luttinger model is used as a basis for the description of the general interacting Fermi gas in one dimension, which will be called 'Luttinger liquid theory', by analogy with Fermi liquid theory. The excitation spectrum of the Luttinger model is described by density-wave, charge and current excitations; its spectral properties determine a characteristic parameter that controls the correlation function exponents. These relations are shown to survive in non-soluble generalisations of the model with a non-linear fermion dispersion. It is proposed that this low-energy structure is universal to a wide class of 1D systems with conducting or fluid properties, including spin chains.

1,451 citations

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TL;DR: In this paper, a dynamical critical exponent is defined for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity.

Abstract: We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent z, which governs the anisotropy between spatial and temporal scaling t {yields} {lambda}{sup z}t, x {yields} {lambda}x; we focus on the case with z = 2. Such theories describe multicritical points in certain magnetic materials and liquid crystals, and have been shown to arise at quantum critical points in toy models of the cuprate superconductors. This work can be considered a small step towards making useful dual descriptions of such critical points.

1,313 citations

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TL;DR: In this paper, the one-dimensional Ising model with a transverse field is solved exactly by transforming the set of Pauli operators to a new set of Fermi operators.

1,266 citations