Showing papers on "Correlation function (statistical mechanics) published in 1982"

Monte Carlo Simulations of One-dimensional Fermion Systems

Abstract: We discuss a new method to perform numerical simulations of one-dimensional systems with fermion and boson degrees of freedom. The method is based on a direct-space, imaginary-time representation of the fermion field. It is fast so that systems having up to 100 sites can easily be simulated. In addition, the method provides an intuitive physical "picture" of the ground state of a one-dimensional many-body system. We discuss in detail how to implement the method and how to compute various physical quantities. In particular, we show how to extend the method to study averages of off-diagonal quantities in an occupation-number representation. To assess the accuracy of our procedure, we apply it to free fermions in one dimension and compare with exact results. We then study a model of spinless interacting fermions and obtain the expected phase structure and behavior of correlation functions. We also consider the extended Hubbard model at various points in its phase diagram and study the behavior of spin-density, charge-density, and pairing correlation functions. We then study the Gross-Neveu model and show how the behavior depends on the number of fermion flavors. Finally, we consider an electron-phonon model and study its behavior both in the one-particle polaron sector and in the half-filled-band case. Along the way we show pictures of the ground-state configurations that give physical insight into the properties of the systems, like charge-density-wave, spin-density-wave, and superconducting states, "fractional charges," and solitons. We conclude by comparing our method with other methods and discuss the possibility of extending it to higher dimensions.

Theory of intermittency

Abstract: The aperiodic or chaotic behavior for one-dimensional maps just before a tangent bifurcation occurs appears as intermittency in which long laminarlike regions irregularly separated by bursts occur. Proceeding from the picture proposed by Pomeau and Manneville, numerical experiments and analytic calculations are carried out on various models exhibiting this behavior. The behavior in the presence of external noise is analyzed, and the case of a general power dependence of the curve near the tangent bifurcation is studied. Scaling relations for the average length of the laminar regions and deviations from scaling are determined. In addition, the probability distribution of path lengths, the stationary distribution of the maps, the correlation function and power spectrum of the map in the intermittent region, and the Lyapunov exponent are obtained.

Integral equation predictions of liquid state structure for waterlike intermolecular potentials

Abstract: An application of our recently developed extended RISM equation formulation to several three‐site models of water is presented. The site–site correlation functions are obtained and compared to available computer simulation results. Further, the variation of liquid state structure with the model site charge is examined. The analysis of these results has demonstrated that the integral equation approach provides a correct qualitative description of the liquid structure, although the amplitudes of most structural features are somewhat less accurate that their positions. Comparison to our earlier results for simpler models suggests that the nature of the quantitative deficiencies of the approach is predictable. The charging study has shown that the development of waterlike structure with increasing site charge follows a qualitatively different pattern for oxygen–oxygen pairs, compared to those involving hydrogen. This is attributed to interference between the amplitudes characteristic of liquid water and of simple liquids. These results suggest that this is the origin of a relatively flat 0–0 correlation function for several models studied in the past, and, further, that such results should not be properly characterized as ’’unstructured.’’

Attenuation of short period seismic waves due to scattering

Abstract: We point out first the inadequacy of the two widely used approaches in calculating the amplitude attenuation of seismic waves in a random medium, the formulation of mean field attenuation and that of the scattering coefficient under the single-scattering approximation Then we calculate the average amplitude attenuation due to scattering in an infinite random slab We slice the random slab into layers of thickness a correlation length and use the Born approximation for each slice to calculate the scattered field To include the effect of multiple scattering, we take the back-halfspace integration of the scattered energy as the energy loss and do energy correction for each successive slice Taking scalar wave approximation for seismic waves, we get a formula for average amplitude attenuation essentially valid for high frequency range (ka»1) The attenuation depends strongly on the form of correlation function of the random inhomogeneities We derive the formulas for Gaussian, exponential and Von Karman correlation functions The frequency dependence of attenuation by our formulation agrees well with experiments

Roughening transitions and the zero-temperature triangular Ising antiferromagnet

Abstract: The zero-temperature triangular Ising antiferromagnet is mapped onto a solid-on-solid (SOS) model. The system undergoes a roughening transition characterised by a critical exponent alpha =1/2, by the absence of excitations in the smooth phase, and by domain wall excitations (stripes) in the rough phase. At infinite SOS temperature the height-height correlation function is explicitly calculated with the aid of known four-point Ising correlations. The authors point out that a certain six-vertex model with a comparable SOS interpretation has an identical critical temperature, critical exponent and critical amplitude. This is in support of existing ideas on university in systems with striped phases.

Decay of Correlations for Infinite Range Interactions in Unbounded Spin Systems

Abstract: In unbounded spin systems at high temperature with two-body potential we prove, using the associated polymer model, that the two-point truncated correlation function decays exponentially (respectively with a power law) if the potential decays exponentially (respectively with a power law). We also give a new proof of the convergence of the Mayer series for the general polymer model.

Critical fan in the antiferromagnetic three-state Potts model

Abstract: The three-state Potts model on a square lattice with general nearest-neighbor interaction and ferromagnetic second-neighbor interaction is studied. At zero temperature the model with antiferromagnetic nearest-neighbor interactions is mapped to the $F$ model. By comparing the excitations generated at nonzero temperature to those that lead to the eight-vertex model we obtain an explicit expression for the critical index describing such excitations and demonstrate the existence of a critical fan for ferromagnetic second-neighbor interactions. The model with purely nearest-neighbor interactions is critical only at zero temperature. Explicit expressions for the scaling indices of the color-color correlation function in the critical phase are also obtained. Phenomenological renormalization-group methods are applied to determine the general boundaries of the critical fan and to verify our expressions for critical indices. A physical system which might be expected to undergo a transition in the same universality class as that of the above model and to exhibit a critical phase is proposed: an equal mixture of krypton and xenon adsorbed on graphite.

Pair correlations in the cluster variation approximation

Abstract: The cluster variation method is used to obtain approximate free energy functions for a binary system in an inhomogeneous field, in order to calculate the Fourier transform of the pair correlation functions. In the two-dimensional square lattice, using the nearest-neighbors square as the basic cluster, the correlation functions are correctly given up to the order 7 in the inverse temperature. The effect of second-neighbor pairs and many-body interactions is investigated.

Finite-size scaling and the two-dimensional XY model

Abstract: Shows that the finite-size scaling assumption, and particularly a conjectured relation involving the exponent eta , are valid in the low-temperature phase of the 2D XY model, order by order in a perturbative expansion of the two-point correlation function.

Comparison of some different approximations in the statistical theory of relative dispersion

Abstract: The effect on the theory of relative dispersion of some different approximations to the two-particle Lagrangian correlation function is examined. Two of these, one due to Taylor, the other to Smith and Hay, are treated in detail. Through numerical solution of the dispersion equations, the influence of the initial cluster size, a number of simple variations of the spatial separation argument of the two-particle correlation function, the number of particles in the cluster and the ratio of Lagrangian to Eulerian integral scales are examined. With the exception of the initial cluster size, which is important in the early stage of growth, these parameters are relatively unimportant, particularly compared to the overall difference between the two approximations. In qualitative agreement with Batchelor's inertial range theory, both the Taylor and Smith-Hay approximations show linear growth at small time with an accelerated growth region at intermediate time. However, between these regions, the Smith-Hay solution shows a region of less-than-linear growth for which there appears to be no observational or theoretical support. This regime is more pronounced, and the difference between the two approximations greater, for initially small clusters. Comparison with suitably documented observations, while not entirely definitive, shows a degree of consistency and suggests the Taylor approximation to be the more appropriate.

Comparison of radial distribution function for silica glass with those for various bonding topologies: Use of correlation function

Abstract: Radial distribution functions (RDF's) calculated from the bonding topologies of quartz, cristobalite, tridymite and a 1412 atom model of silica glass (35 A in diameter) have been compared with the experimental RDF for silica glass. The functions, 4πr3(ϱ(r)−ϱ0), computed over the range 0 < r < 20 A from the known structures of quartz, cristobalite, tridymite and the 1412 atom model have been compared with the corresponding function for silica glass by means of correlation functions, giving 0.26, 0.69, 0.82 and 0.91, respectively (0.00 would indicate no correlation, and 1.00, perfect positive correlation). Cristobalite and tridymite are composed entirely of six-membered rings of silicate tetrahedra, whereas the model contains both six- and five-membered rings in a ratio of 2.6:1. The correlation coefficients suggest that the six-membered rings of the type present in tridymite play a dominant role in silica glass, but that other ring sizes are important and result in the higher correlation coefficient for the 1412 atom model. While the correspondence in RDF's is encouraging, the model RDF does not fit the experimental curve to within the accuracy of the experiment. Perhaps the model is not large enough to represent adequately, in a statistical fashion, all the configurations present in a macroscopic sample.

Lagrangian Monte Carlo simulation of the turbulent motion of a pair of particles

Abstract: A new scheme for simulating the turbulent motion of a pair of particles is presented. Realistic and self-consistent inter-particle correlations are introduced at a fundamental level using a simple parametrization of the two-particle Lagrangian velocity correlation function. For the simple case of stationary homogeneous turbulence in one-dimension, the simulation procedure is in excellent agreement with exact theoretical results. Extension of the method to include more general circumstances is straightforward.

Triplet correlation functions in metallic glasses

Abstract: 'Bond-angle distribution functions-i.e. radial averages over the triplet correlation functions-have been calculated for realistic models of metallic glasses. It is shown that the bond-angle distribution functions are very instructive in elucidating the topological short-range order in non-crystalline structures.

Spin Correlations in Itinerant Electron Magnets

Abstract: Universal expressions are given for the magnetic susceptibility, the average of the squared local amplitude of spin fluctuation: S L 2 ( T ) as a function of temperature and its constituent q -components, and the spatial spin correlation function above T C . Existing experimental data for some of typical ferromagnetic metals are analyzed in terms of the longitudinal and transverse stiffness constants for the spin fluctuation, S L 2 ( T C ), and an effective wave vector cut-off parameter. Possibility for the existence of strong short range order in itinerant magnets such as Fe and Ni is discussed in the light of this analysis.

Isotropic-Nematic Transition: Landau-de Gennes vs Molecular Theory

Abstract: Landau-de Gennes and molecular mean-field descriptions of the isotropic-nematic transition are compared. We use two methods to calculate the order parameter correlation function and show that corrections due to cubic and quartic terms in the Landau expansion are non-negligible. In the first method we apply lowest order diagrammatic perturbation theory using as perturbation both cubic and quartic terms. The second method essentially treats the cubic term to all orders and the quartic term to leading order. A comparison of the results with experiment indicates only qualitative agreement. It is also found that the supercooling temperature T* is different from Tζ, the temperature at which the correlation length diverges. The fact that the corrections are not small and that the results obtained by the two different methods are inconsistent cast grave doubt on the quantitative validity of the Landau-de Gennes approach in its present form. We propose a numerical way to establish contact between the mean...

Light scattering study of the phase transition in sym‐ triazine

Abstract: The ferroelastic phase transition in sym‐triazine C3N3H3 has been investigated by means of Brillouin scattering and correlation spectroscopy. Soft TA modes are observed by Brillouin scattering but a well‐defined central peak could not be found. Near the transition in the high temperature phase a 50% increase in Rayleigh intensity is found. No correlation function was observed in the time domain between 1 and 10−6 s. These results are discussed by a Landau mean field theory and dynamical rotation–translation coupling theory.

Dynamics of a classical hard-sphere gas. II. Numerical results

Abstract: For pt.I see ibid., vol.15, p.2801 (1982). Numerical results for the correlation functions of density, transverse current and energy density of a classical hard-sphere fluid at high density are presented based on a mode-coupling theory developed in a previous paper. The results are compared with an approximate solution of generalised Enskog theory and with results of molecular dynamic experiments. The author finds propagating shear waves above a critical wavenumber and a slowly decaying density correlation function at intermediate wavenumbers, both new qualitative features being in agreement with molecular dynamic results.

Phase transition in the ±J Ising-spin-glass model

Abstract: The two-dimensional $\ifmmode\pm\else\textpm\fi{}J$ model (antiferromagnetic and ferromagnetic bonds at random) is studied by transfer-matrix and Monte Carlo calculations. Large clusters of spins pointing in one direction are found for $0.12lx\ensuremath{\le}0.16$ ($x$ being the concentration of negative bonds). Evidence against a phase transition at finite temperature is found by investigating the correlation function ${〈{S}_{0}{S}_{R}〉}^{2}$..

Raman Scattering: Fast Axial Rotation of Methylhalides and Acetonitrile in the Liquid State

Abstract: The temperature dependence of the degenerate methyl stretching Raman profiles of CH3CN, CH3I, CD3I, CH3Cl, and CH3F and, further, for CH3CN the pressure dependence are investigated. The Raman bands are analysed in terms of the small angle diffusion and the J-diffusion model both with and without Coriolis interaction. The comparison with the small angle diffusion model is carried out in the frequency domain. For the analysis in terms of the J-diffusion model, first experimental orientational correlation functions are calculated. Then, by following theoretical arguments, the overall correlation function is decomposed into two partial correlation functions g(2)1(t) and g(2)2(t). There is limited agreement with previous magnetic relaxation studies on the fast axial spinning motion. In particular, it is found that the partial correlation function g(2)2(t) shows little temperature and pressure dependence, which cannot satisfactorily be accounted for by the existing models.

Generalized Kirchhoff approach to the ocean surface‐scatter communication channel. Part II: Second‐order functions

Abstract: Three second‐order functions which characterize the ocean surface‐scatter communication channel are derived from the transfer function of the ocean surface. These second‐order functions include the two‐frequency correlation function or the two‐frequency mutual coherence function, the scattering function, and the power spectral density function of the scattered acoustic pressure field. These functions are shown to be dependent upon the general form of the directional wavenumber spectrum. Both the slightly rough and very rough surface cases are included. The interrelationships which exist amongst these functions are demonstrated. As an example, the power spectral density function is computed for the very rough surface case using the Neumann–Pierson directional wavenumber spectrum.

Theoretical analysis of the Ising ferromagnetic transition for cubic lattices

Abstract: New relations, the 'i- delta relations', are presented for the evaluation of higher-order critical correlation functions for the three-dimensional spin-1/2 Ising model. The critical temperatures Tc for the cubic lattices are then calculated and are found to be within 1/2% of the results of series analysis. Monte Carlo calculations are performed on the simple cubic lattice, and are found to bear out the theoretical predictions for the correlation functions to within 1.3%, for the basic Tc-determining equations to within 0.5%, and for the i- delta relations to within 2.5%. An earlier theory, which uses the critical correlation function approximation, is critically examined both theoretically and by comparison with the Monte Carlo results.

Macroscopic nucleon-nucleon correlations caused by the bounce-off process in energetic collisions of heavy nuclei

Abstract: Two-particle correlation data are presented for the reaction Ar (800 MeV/nucleon)+Pb The experimental results are analyzed in the nuclear fluid dynamical and in a linear cascade model We demonstrate that the collective hydrodynamical correlations dominate the measured two-particle correlation function for the heavy system studied We discuss the transition from the early stages of the reaction which are governed by few nucleon correlations, to the later stages with their macroscopic flow which can only be reached using heavy colliding systems The sensitivity of the correlation data on the underlying compressional and dissipative processes is analyzed

Determination of the Correlation Function Directly from Slit-Smeared Small-Angle X-ray Scattering Curves

Abstract: A simple technique has been developed for calculating the correlation function directly from small-angle Xray scattering curves obtained with an finfinitely long' primary beam profile. "ihe method is based on expanding the correlation function in a series of zeroorder Bessel functions of the first kind, where the coefficients of the series are proportional to the intensities of the measured curve. The correlation function thus is represented by an analytical expression and can be calculated easily.