Showing papers on "Correlation function (statistical mechanics) published in 1984"
TL;DR: Based on the conformal algebra approach, a general technique for the calculation of multipoint correlation functions in 2D statistical models at the critical point is given in this article, where particular conformal operator algebras are found for operators of the 2D q-component Potts model.
1,317 citations
TL;DR: In this article, it was shown that if rich clusters formed where the primordial density enhancement, when averaged over an appropriate volume, was unusually large, then they give a biased measure of the large-scale density correlation function determiend by the probability distribution of the density fluctuations on a rich cluster mass scale.
Abstract: If rich clusters formed where the primordial density enhancement, when averaged over an appropriate volume, was unusually large, then they give a biased measure of the large-scale density correlation function determiend by the probability distribution of the density fluctuations on a rich cluster mass scale. If this distribution was Gaussian, the correlation function is amplified. The amplification for rich clusters is estimated to be eaual about ten and predicted trend of amplification with richness agrees qualitatively with that observed. Some implications of these results for the large-scale density correlations are discussed.
1,220 citations
TL;DR: For the Q -state Potts model, the authors showed that η = 2 (3v − 1), and for the O( N ) model (−2 ⩽ N⩽ 2), η was shown to be 2 (2v−1) (4v−2).
1,020 citations
TL;DR: In this article, the authors calculate the evolution of cosmological density correlation functions to lowest nonvanishing order in perturbation theory for an initially random Gaussian distribution, which is consistent with observations in the nonperturbative regime.
Abstract: I calculate the evolution of cosmological density correlation functions to lowest nonvanishing order in perturbation theory for an initially random Gaussian distribution. The three-point function so obtained scales with size as in the continuous hierarchy model, but there is a residual nontrival dependence on shape of the reduced three-point amplitude Q. The average value Q-bar = 34/21-(1/6)..gamma.. is consistent with observations in the nonperturbative regime. The four-point function is also hierarchical in form, with amplitudes R/sub a/ = (34/21)/sup 2/ and R-bar/sub b/ = 682/189. The perturbation expansion in fact gives kappa/sub N/proportionalxi/sup N/-1 for the reduced correlation function kappa/sub N/ to all orders N. A graphical technique enumerates the terms which appear in kappa/sub N/.
438 citations
TL;DR: In this paper, the authors considered the critical exponent γ associated with the expected cluster sizex and the structure of then-site connection probabilities τ =τn(x 1,..., xn) and showed that quite generally γ⩾ 1.
Abstract: Various inequalities are derived and used for the study of the critical behavior in independent percolation models. In particular, we consider the critical exponent γ associated with the expected cluster sizex and the structure of then-site connection probabilities τ=τn(x1,..., xn). It is shown that quite generally γ⩾ 1. The upper critical dimension, above which γ attains the Bethe lattice value 1, is characterized both in terms of the geometry of incipient clusters and a diagramatic convergence condition. For homogeneousd-dimensional lattices with τ(x, y)=O(¦x -y¦−(d−2+η), atp=p
c, our criterion shows that γ=1 if η> (6-d)/3. The connectivity functions τn are generally bounded by tree diagrams which involve the two-point function. We conjecture that above the critical dimension the asymptotic behavior of τn, in the critical regime, is actually given by such tree diagrams modified by a nonsingular vertex factor. Other results deal with the exponential decay of the cluster-size distribution and the function τ2
(x, y).
315 citations
TL;DR: In this paper, the authors derived the limit distribution of the covariance function for the least squares estimates of the parameters in an autoregressive process with a finite variance but an infinite variance but a infinite fourth moment.
Abstract: : Document describes a moving average process which have regularly varying tail probabilities with index alpha 0. The limit distribution of the sample covariance function is derived in the case that the process has a finite variance but an infinite variance but an infinite fourth moment. Furthermore, in the infinite variance case (0 alpha 2), the sample correlation function is shown to converge in distribution to the ratio of two independent stable random variables with indices alpha and alpha/2, respectively. This result immediately gives the limit distribution for the least squares estimates of the parameters in an autoregressive process. (Author)
306 citations
TL;DR: In this article, a formula for the two-pion correlation function is derived for an arbitrary chaotic source when the emission spectrum from each point in space-time is known, and the experimental fact that pions with high momentum in the center-of-mass frame are more correlated than low-momentum pions is explained by a collective expansion of the source.
Abstract: A formula for the two-pion correlation function is derived for an arbitrary chaotic source when the emission spectrum from each point in space-time is known. The experimental fact that pions with high momentum in the center-of-mass frame are more correlated than low-momentum pions is explained by a collective expansion of the source. A simple model illustrates how the pion correlations can be used to measure the expansion velocity of a nuclear fireball.
260 citations
TL;DR: In this article, the inverse scattering method was used for the calculation of correlation functions in completely integrable quantum models with the R-matrix of XXX-type, including the Bose-gas and the Heisenberg XXX-model.
Abstract: The inverse scattering method approach is developed for calculation of correlation functions in completely integrable quantum models with theR-matrix of XXX-type. These models include the one-dimensional Bose-gas and the Heisenberg XXX-model. The algebraic questions of the problem are considered.
227 citations
IBM1
TL;DR: In this article, a four-body interaction potential for water molecules is derived for the correlation function g(OO), for the X-ray and neutron-beam scattering intensities, and for the enthalpy.
114 citations
TL;DR: In this article, the authors consider dilute suspensions of homogeneous polydisperse spherical particles for which the Rayleigh-Gans-Debye (RGD) approximation is valid.
Abstract: We consider dilute suspensions of homogeneous polydisperse spherical particles for which the Rayleigh–Gans–Debye (RGD) approximation is valid. For two model particle size distributions we calculate the dependence on scattering vector Q of the average scattered intensity I(Q) and the effective diffusion coefficient De(Q) obtained from the first cumulant measured by photon‐correlation spectroscopy. If the mean particle radius R is large enough (≳170 nm) that the intensity form factor P(QR) shows at least one minimum in the accessible range of Q, we find that De(Q) exhibits a characteristic variation with Q which is very sensitive to the sample polydispersity. Under favorable conditions it should be possible to measure polydispersities (standard deviation/mean size) as small as 0.01. These theoretical considerations are supported, at least qualitatively, by experiment. We also discuss briefly the effect of relaxing the RGD approximation and the implications of this work for the more common PCS probes of polydispersity such as Laplace transformation of the light scattering correlation function.
110 citations
TL;DR: In this paper, the effect of the mutual Coulomb repulsion of two like-charged pions, and of the pion-nuclear Coulomb interaction, on the two-pion correlation function is analyzed.
Abstract: An application of intensity interferometry to relativistic heavy ion collisions is reported. The correlation between two like-charged pions is used to study the reactions Ar+KC1..-->..2..pi../sup + -/+X and Ne+NaF..-->..2..pi../sup -/+X, both at an incident beam energy of 1.8A GeV. Source sizes and lifetimes are measured and compared to the predictions of simple geometric models and of Monte Carlo cascade calculations. There appears to be a substantial coherent component of the pion source, although measurement is complicated by the presence of final state interactions. A detailed discussion of the techniques of intensity interferometry is also presented. The generation of uncorrelated background events is discussed, along with the influence of the correlation on the background and the prescription for its removal. The statistical errors in the background spectrum are examined and found to have nontrivial implications for the analysis. The effect of the mutual Coulomb repulsion of the two pions, and of the pion-nuclear Coulomb interaction, on the two-pion correlation function is analyzed. The impact parameter bias resulting from a two-pion trigger is calculated and found to be substantial. Finally, a simple model for the interpretation of Gaussian source parameters is presented and compared to the predictions of Monte Carlo cascade calculations.
TL;DR: In this paper, the authors express the N-point rich cluster correlation function in terms of the two-point RCF in a model where rich clusters formed wherever suitably averaged primordial energy density fluctuations are unusually large.
Abstract: The authors express the N-point rich cluster correlation function in terms of the two-point rich cluster correlation function in a model where rich clusters formed wherever suitably averaged primordial energy density fluctuations are unusually large. The validity of the results is not restricted to regions where the connected (reduced) N-point correlation functions are small compared with unity.
TL;DR: The Artemia results show that the translational diffusion coefficient of the mobile water fraction was greatly reduced from that of pure water, and the line width was determined mainly by the rotational motion, which was also substantially reduced from the pure water value as determined from dielectric relaxation studies.
TL;DR: In this article, the two-time photon-number correlation function for fluorescent light homodyned with coherent light was derived, and the falloff in squeezing with time delay was evaluated.
TL;DR: In this article, anisotrope sur la fonction de correlation de champ polarise de la lumiere diffusee de facon quasielastique a partir de solutions.
Abstract: Modele theorique pour l'influence de la diffusion translationnelle anisotrope sur la fonction de correlation de champ polarise de la lumiere diffusee de facon quasielastique a partir de solutions
TL;DR: In this paper, the equation of state of hard oblate spherocylinders has been calculated for a wide range of densities and reduced core diameters (l* = l/σ, where l and σ are the diameter of the disc core and sphero cylinder thickness, respectively) using the Monte Carlo method.
Abstract: The equation of state of hard oblate spherocylinders has been calculated for a wide range of densities and reduced core diameters (l* = l/σ, where l and σ are the diameter of the disc core and spherocylinder thickness, respectively) using the Monte Carlo method. The most accurate representation of the data is given by a resummed virial series equation of state based on virial coefficients up to the sixth. Other equations are tested and are found to be less accurate. The fluid structure is discussed in terms of the centres pair correlation function, the surface-surface correlation function, and the coefficients in the spherical harmonic expansion of the pair correlation function. At high densities, neighbouring molecules pack into a short ranged shell structure about a central molecule, in analogy with the hard sphere fluid. We also report Monte Carlo calculations for a fluid of oblate spherocylinders with the addition of a point quadrupole, and examine the effect of the quadrupole-quadrupole forces on bot...
TL;DR: In this article, a special-purpose molecular-dynamics hardware processor was used to simulate two-dimensional Lennard-Jones systems of 10 864 particles, and the asymptotic behavior of the orientational correlation function was found to be in accordance with a first-order melting transition.
Abstract: With the aid of a special-purpose molecular-dynamics hardware processor the authors have simulated two-dimensional Lennard-Jones systems of 10 864 particles. The asymptotic behavior of the orientational correlation function is found to be in accordance with a first-order melting transition.
TL;DR: In this article, an extension of the field emission fluctuation method for studying the diffusion of adsorbates on metal surfaces to the measurement of anisotropic diffusion is described, which consists of using a long, narrow rectangular slit as probed region.
TL;DR: In this paper, Monte Carlo methods are employed to measure the internal energy, sublattice magnetization, and spin-spin correlation function of the fcc antiferromagnetic Ising model as a function of temperature.
Abstract: Monte Carlo methods are employed to measure the internal energy, sublattice magnetization, and spin-spin correlation function of the fcc antiferromagnetic Ising model as a function of temperature. The internal energy of both the ordered and disordered phases is fitted by appropriate series expansions, and the free energy is obtained analytically from the series. The ordering transition is seen to be of first order with a transition temperature of 1.736\ifmmode\pm\else\textpm\fi{}0.001 in units of the nearest-neighbor coupling $J$. These results are compared with earlier approximations of the model, in particular, the low-temperature series expansion and the Kikuchi tetrahedron approximation, and other Monte Carlo results. The spin-spin correlation function was measured in the disordered phase up to eight lattice spacings in the [100] direction. The correlation length at the transition is found to be $\ensuremath{\sim}2.5a$. The behavior of the correlation length is approximately mean-field-like.
TL;DR: On obtient la fonction de correlation spin spin-spin X(m,n) dans le reseau carre d'Ising sous forme d'un developpement en serie different du deVELoppement bien connu.
Abstract: On obtient la fonction de correlation spin-spin X(m,n) dans le reseau carre d'Ising sous forme d'un developpement en serie different du developpement bien connu
TL;DR: In this article, a simple approximation for the average correlation function of hard convex bodies is proposed based on the knowledge of the total correlation functions of equivalent hard spheres, which yields very good predictions for the third and fourth virial coefficients of the prolate and oblate hard spherocylinders.
Abstract: A simple approximation for the average correlation function of hard convex bodies is proposed based on the knowledge of the total correlation function of equivalent hard spheres. The proposed relationship yields very good predictions for the third and fourth virial coefficients of the prolate and oblate hard spherocylinders, and for the contact values of the average correlation functions of prolate spherocylinders and of their mixtures with hard spheres. The approximation reproduces fairly well the dependence of the average correlation functions on distance. The two parameter equation of state formulated on its basis predicts the compressibility factor of hard bodies of different shapes with fair accuracy and appears to be more general than the relationships available up to date.
TL;DR: In this paper, a modele theorique pour etudier l'influence de la diffusion translationnelle anisotrope and the flexibilite d'un filament sur la fonction de correlation de la lumiere diffusee par des solutions de filaments tres longs semiflexibles is presented.
Abstract: Modele theorique pour etudier l'influence de la diffusion translationnelle anisotrope et la flexibilite d'un filament sur la fonction de correlation de la lumiere diffusee par des solutions de filaments tres longs semiflexibles
TL;DR: In this paper, the authors provide a straightforward and physically suggestive scheme for treating the bulk properties of interacting particles characterized by arbitrary charge, axial ratio and concentration, which involves a marriage of Onsager's charge "smearing" optimization with a variational statement of the mean spherical approximation.
Abstract: A great deal of effort has been devoted for many years to the statistical thermodynamics of interacting charged particles having spherical symmetry, e.g., simple electrolyte solutions, fluid plasmas, and micellized suspensions of ionic surfactants. In the present work we provide a straightforward and physically suggestive scheme for treating the bulk properties of interacting particles characterized by arbitrary charge, axial ratio and concentration. The basic idea involves a marriage of Onsager’s charge ‘‘smearing’’ optimization with a variational statement of the mean spherical approximation. In particular the direct correlation function is shown to be described accurately by the pair interaction energy between smeared charge distributions. After illustrating this approach for point particles (one and multicomponent plasmas), we generalize it to line charges of arbitrary length l. A simple analytical theory of the isotropic→nematic transition in this system is presented for the large l, high density reg...
TL;DR: In this article, the Fourier transform of the density-density correlation function is used to relate measurements of the angular dependence of scattered light to material structure parameters, and the fit shows that light scattering from aerogels may be interpreted as having two origins; one from the small scale structure of linked particles that comprise the material and the second due to weak fluctuations in the average density of the microporous structure over distances significantly larger than the pore size.
Abstract: This paper reports a recent advance in the understanding of the structure of microporous optical materials such as aerogel through the interpretation of light scattering data. The Fourier transform of the density-density correlation function is used to relate measurements of the angular dependence of scattered light to material structure parameters. The results of the approach fit the unusual dependence of the intensity of scattered light as a function of angle for two polarizations. The fit shows that light scattering from aerogels may be interpreted as having two origins; one from the small scale structure of linked particles that comprise the material, and the second due to weak fluctuations in the average density of the microporous structure over distances significantly larger than the pore size.
TL;DR: A previously developed microscopic theory for the wavevector-dependent spin susceptibility chi (q) of paramagnetic iron based on the Hubbard-Hasegawa approach has been applied to nickel.
Abstract: A previously developed microscopic theory for the wavevector-dependent spin susceptibility chi (q) of paramagnetic iron based on the Hubbard-Hasegawa approach has been applied to nickel. The equal-time spin-spin correlation function evaluated with the use of the calculated chi (q) and the classical fluctuation-dissipation theorem accounts well for the observed feature in the integrated neutron scattering intensity. The magnitude of local magnetic moments and the spatial correlation function are also calculated by summing chi (q) over the FCC first Brillouin zone, and they are shown to be consistent with experimental data.
TL;DR: In this paper, a model of the vertical structure of turbulence in the convective boundary layer is presented based on representation of the fluctuating velocity components by trigonometric orthogonal functions.
Abstract: A model is presented of the vertical structure of turbulence in the convective boundary layer. The model is based on representation of the fluctuating velocity components by trigonometric orthogonal functions. The vertical velocity component is represented by a sine and the horizontal by a cosine expansion. The sine representation of the w component ensures that w = 0 at z = 0. The expansion coefficients are uncorrelated if the sine functions are eigenfunctions of the vertical correlation function.
A simple form, based on the inertial sub-range, is adapted for the energy spectrum.
Constant parameters of the model are evaluated from the surface layer measurements of the wind velocity variances, and it is shown that the model agrees with the measured vertical structure of variances through the whole boundary layer.
TL;DR: In this paper, the generalized Trotter formula is used to map the two-dimensional spin-1/2 XY model onto several three-dimensional Ising models with complicated many-spin interactions.
Abstract: The generalized Trotter formula is used to map the two-dimensional spin-1/2 XY model onto several three-dimensional Ising models with complicated many-spin interactions. This hierarchy of Ising-like models is studied by means of analytic and Monte Carlo techniques. We demonstrate that the sequence of these Ising models can be used to calculate accurately the thermodynamics of the two-dimensional spin-1/2 XY model. By calculating the specific heat, spin correlation functions, susceptibilities and a disorder parameter, we address the question of the nature of the phase transition in the two-dimensional spin-1/2 XY model.
TL;DR: In this paper, the authors review the relation between the relaxation of extensive thermodynamic and of viscoelastic functions, and the physical basis and results of two kinetic theories of volume relaxation are summarized.
Abstract: We review first recent results concerning the relation between the relaxation of extensive thermodynamic and of viscoelastic functions. In the underlying theory a central role is assigned to a particular excess-free volume function h. It was originally introduced in a theory of the equilibrium melt. The time dependence of h can then be derived from volume (or enthalpy) recovery data and serves to predict other quantities, such as mean-square density fluctuations and viscoelastic-temperature shift factors during the aging process. Next the physical basis and results of two kinetic theories of volume relaxation are summarized. In both approaches the h-function is employed as an expression of the molecular dynamics in the drive to equilibrium. The first describes a gradual elimination of free-volume gradients through a diffusion process, characterized by a diffusion parameter, varying with the local free volume in accord with a Doolittle relation. The second, a stochastic theory, derives expressions for the matrix of transition rates between different free-volume states, the resulting spectrum of retardation times, and the size distribution of free volume in the relaxing system. Satisfactory agreement between observed and predicted volume recovery of poly(vinyl acetate) ensues. In the limit of an infinitesimal temperature jump, both theories yield a Williams-Watts correlation function as an approximate interpolation expression. The exponent β, however, varies in time with a constant value of approximately 0.60 over a limited time interval.
TL;DR: In this article, a modified hypernetted chain equation is used to extend the simulation results for the radial distribution function g(r) to distances larger than the basic simulation cell.
Abstract: We explore a new procedure for extending the simulation results for the radial distribution function g(r) to distances larger than the basic simulation cell The method is based on the modified hypernetted chain equation The bridge function in this equation is initially approximated by results for hard sphere fluids and then subsequently modified to bring the computed g(r) into agreement with the available simulation data The method appears to be successful for densities up to about 90% of the triple‐point density Applications to the Lennard‐Jones fluid are presented