Showing papers on "Correlation function (statistical mechanics) published in 1994"
219 citations
TL;DR: In this paper, a comprehensive review on the various correlation functions for coherent electronic or classical wave transmission through a disordered scattering medium, in the diffusive limit, is presented, where λ is the wavelength, l∗ is the transport mean free path, and Lφ is the phase coherence length.
146 citations
TL;DR: The low-q maximum in the I(q) curve is here directly quantitatively accounted for, without introducing any phenomenological ad hoc term to describe the intercluster correlations.
Abstract: Numerical simulations of gel formation by off-lattice diffusion-limited cluster-cluster aggregation (DLCA) of identical spherical particles in a cubic box are performed. Both the correlation function g(r) and the small-angle scattering function S(q), which is related to the Fourier transform of g(r)-1, are calculated for the resulting gel structure which is made of connected fractal clusters. In addition to the short-range features already described in a previous paper, it is found that g(r) goes through a minimum before tending to unity for large r values. As a consequence the scattering function S(q) exhibits a maximum at small q values. After multiplying S(q) by the form factor P(q), the intensity curve I(q) is calculated and its behavior is found to be in good agreement with small-angle neutron-scattering experiments on silica aerogels of various densities. In contrast with previous approaches, the low-q maximum in the I(q) curve is here directly quantitatively accounted for, without introducing any phenomenological ad hoc term to describe the intercluster correlations.
131 citations
TL;DR: A parameter-free relation is given between total cross sections and slope parameters, which is shown to be remarkably valid up to the highest energies for which data exist.
Abstract: Total cross sections and logarithmic slopes of the elastic scattering cross sections for different hadronic processes are calculated in the framework of the model of the stochastic vacuum. The relevant parameters of this model, a correlation length and the gluon condensate, are determined from scattering data, and found to be in very good agreement with values coming from completely different sources of information. A parameter-free relation is given between total cross sections and slope parameters, which is shown to be remarkably valid up to the highest energies for which data exist.
119 citations
01 Jan 1994
TL;DR: The problem of correlation may be described as the investigation of those properties of multivariate distributions which characterize these distributions, i.e., do not occur for univariate distributions as mentioned in this paper.
Abstract: The problem of correlation may be described as the investigation of those properties of multivariate distributions which characterize these distributions, i.e., do not occur for univariate distributions. These properties depend above all on the relationships of the variables to each other. From the totality of those properties which belong to the topic of correlation one particular class of properties will be considered more closely.
118 citations
TL;DR: In this article, a special correlation function in the isotropic spin-1 2 Heisenberg antiferromagnet is considered, i.e., the probability of finding a ferromagnetic string of (adjacent) spins in the ground state.
109 citations
TL;DR: In this article, the effects of the Taylor microscale based Reynolds number on turbulence in the inertial range were studied in the atmospheric surface layer of a large wind tunnel, and the intermittency exponent μ, estimated from the correlation function of energy dissipation, was found to be independent of Reynolds number and approximately equal to 0.20.
Abstract: Characteristics of turbulence in the inertial range are experimentally studied in the atmospheric surface layer over the range of the Taylor microscale based Reynolds number Rλ≊(2.8–12.7)×103 and in a large wind tunnel (in a mixing layer at Rλ≊2.0×103 and a return channel at Rλ≊3.2×103). The intermittency exponent μ, estimated from the correlation function of energy dissipation Ree(r)=〈e(x)e(x+r)〉∝r−μ, is found to be independent of Reynolds number and approximately equal to 0.20. No ‘‘measurable’’ deviation from the −5/3 exponent in the ‘‘five‐thirds’’ law is found. On the other hand, the Kolmogorov constant C in this law is found to be weakly dependent on Rλ. This dependence is well described by the power law C∝R−μ/2λ≊R−0.10λ at μ≊0.20.
98 citations
TL;DR: In this paper, a molecular dynamics simulation of a united-atom polyethylene model was performed to study the short time dynamics of polymer liquid and glass, and the simulation runs lasting up to 5 ns were performed at ten temperatures above and below the estimated glass transition temperature.
Abstract: Molecular dynamics simulation of a united‐atom polyethylene model was performed to study the short time dynamics of polymer liquid and glass. Simulation runs lasting up to 5 ns were performed at ten temperatures above and below the estimated glass transition temperature. Quantities evaluated for the purpose of studying the dynamics include: segmental mean square displacement, van Hove space–time correlation function, intermediate scattering function, dynamic structure factor, and velocity autocorrelation function. Many of the features observed agree well with those obtained from quasielastic neutron scattering measurements with polymeric and nonpolymeric liquids. The dynamics in the time scale between 0.01 and 103 ps clearly divides itself into two regimes; the fast process, occurring below about 1.5 ps, is Debye‐like, while the slower process follows the Kohlrausch–Williams–Watts function. The former probably arises from motion of segments within a cage, and the latter from the α relaxation involving coo...
95 citations
TL;DR: In this paper, the phase transition from an isotropic to a nematic phase for a classical fluid of hard ellipsoids has been studied using a version of a theory originally due to Onsager and by computer simulation.
Abstract: The phase transition from an isotropic to a nematic phase for a classical fluid of hard ellipsoids has been studied using a version of a theory originally due to Onsager and by computer simulation. In the proposed form of the Onsager theory for the Helmholtz free energy, both the second and the third virial coefficients are treated exactly, but the fourth and higher virials are resummed in a manner consistent with the Carnahan-Starling equation of state for hard spheres. This same approach is applied to the calculation of the direct correlation function. A comparison of order parameters, transition densities and pressures calculated by simulation and by the resummed Onsager theory, suggests the following. (i) For 10 : 1 prolate hard ellipsoids, resumming the fourth and higher virial coefficients (rather than simply neglecting them) degrades the agreement by overestimating the importance of the higher virials. (ii) For 5 : 1 prolate and 1 : 5 oblate hard ellipsoids, the resummation yields a considerable im...
82 citations
TL;DR: The use of scanning confocal laser microscopy to measure correlation functions in both space and time is described, providing a straightforward means of performing high resolution correlation analysis of molecular motions with available instrumentation.
74 citations
TL;DR: In this article, the authors show that the fractal dimension of extensive chaos is determined by the average spatial disorder as measured by the spatial correlation length associated with the equal-time two-point correlation function, a measure of the correlations between different regions of the system.
Abstract: SUSTAINED nonequiibrium systems can be characterized by a fractal dimension D⩾0, which can be considered to be a measure of the number of independent degrees of freedom1. The dimension D is usually estimated from time series2 but the available algorithms are unreliable and difficult to apply when D is larger than about 5 (refs 3,4). Recent advances in experimental technique5–8 and in parallel computing have now made possible the study of big systems with large fractal dimensions, raising new questions about what physical properties determine D and whether these physical properties can be used in place of time-series to estimate large fractal dimensions. Numerical simulations9–11 suggest that sufficiently large homogeneous systems will generally be extensively chaotic12, which means that D increases linearly with the system volume V. Here we test an hypothesis that follows from this observation: that the fractal dimension of extensive chaos is determined by the average spatial disorder as measured by the spatial correlation length e associated with the equal-time two-point correlation function —a measure of the correlations between different regions of the system. We find that the hypothesis fails for a representative spatiotemporal chaotic system. Thus, if there is a length scale that characterizes homogeneous extensive chaos, it is not the characteristic length scale of spatial disorder.
TL;DR: In this paper, a theory for diffusion-limited charge transfer on a non-fractally rough electrode was developed for arbitrary one-and two-dimensional surface profiles, and the perturbation expressions were obtained for concentration, current density and measured diffusion limited current.
TL;DR: In this paper, a correlation transfer equation for multiple scattering of light through suspensions of diffusing particles is derived from multiple scattering theory, and a three-term Legendre expansion for the angularly dependent single scattering function in the correlation integral equation is used to obtain approximate numerical solutions for the correlation function.
Abstract: A correlation transfer equation for multiple scattering of light through suspensions of diffusing particles is derived from multiple scattering theory. Because of the formal similarity between the correlation equation and the radiative transfer equation, radiative transport solution techniques are applied to obtain solutions for the field correlation function in isotropic one-dimensional media. A three-term Legendre expansion for the angularly dependent single scattering function (g') in the correlation integral equation is used to obtain approximate numerical solutions for the correlation function. Graphical results are presented for the correlation in both the forward and backward directions for a finite medium and for backscattering in the case of an infinite medium. Experimental results are also presented and they show improved agreement with the three-term Legendre expansion of g' as compared to the one or two-term expansions. Correlation transfer results are shown to agree well with both the diffusion limit and the single scattering limit predictions. The motion of particles in fluid/particle suspensions gives rise to temporal fluctuations in the intensity of multiply scattered light. From the measured temporal autocorrelation functions, one can in principle, determine fluid/particle properties such as particle diameter, fluid viscosity, and diffusion constants. These measurements can be used to characterize a variety of suspensions such as gels and paint. However, for accurate characterization, the suspensions must be very dilute so that the Born approximation may be employed.' For optically dense suspensions, the diffusion approximation has successfully been used to study the time dependence of the intensity fluctuations in what has been termed diffusive wave spectroscopy (DWS).2.3 Another related theoretical approach that has been developed to calculate the temporal autocorrelation function of multiply scattered light was employed by Stephen4 using a diagram- matic description of the scattering from the random fluctuations in the dielectric constant. The propagation of light is still assumed to be diffusive in Stephen's derivations. Arbitrary orders of scattering could not be predicted and modeled by either of the two diffusion methods above. For semi-infinite media, experimental results show that the backscattered correlation function exhibits an exponential decay in the square root of delay time over the full range of the delay times measured.2.3.5 The theoretical diffusive wave results (DWS) for backscattering do produce precisely this decay rate for boundary conditions assuming a single deposition depth for the incident light. If the deposition depth is exponentially distributed and decaying with increasing distance from the surface of the medium (Beer's law), the predicted correlation function shows even greater departures from the experimentally observed exponentiality.6 This problem has been attributed to the continuous light path length distribution assumption made in DWS. This assumption includes paths which tend to zero length and correspond to very slowly decaying correlation functions at large delay times. These decay rates are much slower than the expected decay rate for backscat- tering and so contribute to a theoretical anomaly. This is partially remedied by the assertion that the deposition depth distribution is narrowly distributed near the average scattering length' (not following Beer's law). However, this result is essentially the original DWS result described above with the deposition depth identified as the average scattering length.
TL;DR: In this paper, an integral equation for the two-point intermolecular correlation function in molecular liquids is derived, expressed as a two molecule average over a Boltzmann factor involving a "bare" site-site interaction.
Abstract: We employ density functional methods to derive an integral equation for the two‐point intermolecular correlation function in molecular liquids. This radial distribution function is expressed as a two molecule average over a Boltzmann factor involving a ‘‘bare’’ site–site interaction, plus a pairwise additive, intermolecular, medium induced potential which mimics the remaining molecules in the system. This theory is formally exact in the low density limit. While the theory is valid in general for large molecule and polymer liquids, we demonstrate its use here for the case of the simple diatomic liquid. In this application, good agreement is found at all densities for the radial distribution function and equation‐of‐state when compared with computer simulations. Furthermore, the theory appears to give pressures that are more thermodynamically consistent than those obtained with reference interaction site model (RISM) theory.
TL;DR: The phase separation kinetics of a two-dimensional binary mixture at critical composition confined between (one-dimensional) straight walls which preferentially attract one component of the mixture is studied for a wide range of distancesD between the walls.
Abstract: The phase separation kinetics of a two-dimensional binary mixture at critical composition confined between (one-dimensional) straight walls which preferentially attract one component of the mixture is studied for a wide range of distancesD between the walls. Following earlier related work on semiinfinite systems, two choices of surface forces at the walls are considered, one corresponding to an incompletely wet state of the walls, the other to a completely wet state (forD→∞). The nonlinear Cahn-Hilliard-type equation, supplemented with appropriate boundary conditions which account for the presence of surfaces, is replaced by a discrete equivalent and integrated numerically. Starting from a random initial distribution of the two species (say,A andB), an oscillatory concentration profile rapidly forms across the film. This is characterized by two thin enrichment layers of the preferred component at the walls, followed by adjacent depletion layers. While in these layers phase separation is essentially complete, the further oscillations of the average composition at distanceZ from a wall get rapidly damped asZ increases toward the center of the film. This structure is relatively stable for an intermediate time scale, while the inhomogeneous structure in the center of the film coarsens. The concentration correlation function in directions parallel to the walls (integrated over allZ) and the associated structure factor (describing small-angle scattering from the film) exhibit a scaling behavior, similar to bulk spinodal decomposition, and the characteristic length scale grows with time asl
‖, wherea is close to the Lifshitz-Slyozov value 1/3, and the coefficients α, β depend on film thickness only weakly. Only when one considers the local correlation function at distances close to the walls are deviations from scaling observed due to the competing effects of the grwing surface enrichment layers. However, at very late times [whenl
‖
(t) becomes comparable toD] this bulklike description breaks down, and a concentration distribution is expected to be established which is a superposition of domains separated by interfaces perpendicular to the walls, the one type of domain being rich inA and nearly homogeneous, and the other poor inA except for two thin enrichment layers at the walls.
TL;DR: In this paper, the second-order terms in the expansion in the variance σ2 of normally distributed log conductivity were derived for media of anisotropic structure, and the dependence of the effective conductivity on the correlation structure was illustrated for Gaussian and exponential autocovariances of log conductivities.
Abstract: Properties of the effective conductivity tensor Keff are studied by deriving the second-order terms in its expansion in the variance σ2 of normally distributed log conductivity. It is shown that for media of anisotropic structure, the components of the effective conductivity tensor are expressed by a functional of the log conductivity covariance; that is, it depends on the shape of the correlation function and not only on anisotropy ratios, variance σ2, and space dimensions. However, the trace of Keff is independent of the log conductivity autocovariance, and for a given mean conductivity depends only on σ2. The dependence of the effective conductivity on the correlation structure is illustrated for Gaussian and exponential autocovariances of log conductivity and for two- and three-dimensional flows.
TL;DR: In this article, the results of a Monte Carlo simulation study of the cavity correlation function y(r) for the soft sphere fluid were presented, where the Ornstein-Zernike relationship was used to determine the direct correlation function c(r), which is derived from simulations of the total correlation function h(r).
Abstract: The soft sphere fluid is of interest as a possible reference fluid since, like the hard sphere fluid, the configurational properties and distribution functions scale with a single parameter. In this paper we present the results of a Monte Carlo simulation study of the cavity correlation function y(r) for the soft sphere fluid. Using the Ornstein–Zernike relationship, the direct correlation function c(r) is determined from simulations of the total correlation function h(r). The bridge function B(r) is calculated by difference. We provide a correlation of the bridge function and demonstrate the usefulness of this reference fluid by calculating some properties of the Lennard‐Jones fluid using reference hypernetted chain (HNC) and Rosenfeld and Blum’s prescription for the bridge function state point. The soft sphere bridge function is also compared with the bridge functions for the hard sphere and Lennard‐Jones fluids. Finally, it is demonstrated that closures similar to the Percus–Yevick (PY) closure are poor at short range and should only be valid for repulsive fluids; observations are made concerning modifications of the PY closure for repulsive and attractive fluids.
TL;DR: In this article, the small amplitude response of stochastic one-body theories, such as the Boltzmann-Langevin approach, is studied for unstable nuclear matter in two dimensions.
01 Jan 1994
TL;DR: A review of Langevin dynamics simulations, with emphasis on the practical details, is presented in this article, where the topics include parametrisation of the friction constant and related hydrodynamic theory; choice of algorithms and estimation of systematic and statistical error; calculation of transition rates from time correlation functions and the Kramers theory of barrier crossing; reorientational correlation functions; application to lipid bilayers, including the analysis of NMR spin-lattice relaxation times from simulations.
Abstract: A review of Langevin dynamics simulations, with emphasis on the practical details, is presented. The topics include (i) parametrisation of the friction constant and related hydrodynamic theory; (ii) choice of algorithms and estimation of systematic and statistical error; (iii) calculation of transition rates from time correlation functions and the Kramers theory of barrier crossing; (iv) reorientational correlation functions; (v) application to lipid bilayers, including the analysis of NMR spin-lattice relaxation times from simulations. Topics (ii)-(iv) are illustrated with simulations of a particle in a harmonic potential, a particle in a bistable potential, and a dimer in a Maier-Saupe potential, respectively. The FORTRAN programs for these examples are included.
TL;DR: For spin models with O(2)-invariant ferromagnetic interactions, the Patrascioiu-Seiler constraint is |arg(S(x)·S(y)|⩽θ 0 for all |x−y| = 1 as discussed by the authors, and it is shown that in two-dimensional systems of two-component spins the imposition of such contraints with θ 0 small enough indeed results in the suppression of exponential clustering.
Abstract: For spin models withO(2)-invariant ferromagnetic interactions, the Patrascioiu-Seiler constraint is |arg(S(x))−arg(S(y))|⩽θ0 for all |x−y|=1. It is shown that in two-dimensional systems of two-component spins the imposition of such contraints with θ0 small enough indeed results in the suppression of exponential clustering. More explicitly, it is shown that in such systems on every scale the spin-spin correlation function obeys 〈S(x)·S(y)〉≥1/(2|x−y|2) at any temperature, includingT=∞. The derivation is along the lines proposed by A. Patrascioiu and E. Seiler, with the yet unproven conjectures invoked there replaced by another geometric argument.
TL;DR: In this article, a gradientless correlation functional is derived within the Kohn-Sham density-functional theory (DFT) based on a spin-polarized pair correlation function of Colle-Salvetti type.
Abstract: A gradientless correlation functional is derived within the Kohn-Sham density-functional theory (DFT) based on a spin-polarized pair correlation function of Colle-Salvetti type. The functional involves explicitly only the antiparallel spin correlation while parallel-spin correlation is taken into account indirectly in a manner providing self-interaction-free results. Combined with the local-spin-density (LSD) exchange, and with the nonlocal exchange functional of Becke, the resulting DFT schemes are tested on a set of atoms and small molecules. Compared to experiment, the calculated correlation energies of molecules are on average better than those obtained by other functionals employed in the deMon code [A. St.-Amant and D. R. Salahub, Chem. Phys. Lett. 169, 387 (1990)]: Becke-Perdew (88) and Perdew-Wang (91). For atoms the correlation functional gives slightly worse results than Perdew-Wang (91), but substantially better than the LSD approximation. The corresponding binding energies are on average slightly better than those obtained by the existing gradient-corrected schemes and in excellent agreement with experiment.
TL;DR: In this paper, the mean square fluctuation width of a single step on the vicinal surface, denoted by Δ 2 ( y ) (y : distance along the step), is calculated based on the terrace-step-kink picture.
Abstract: Mean-square fluctuation width of a single step on the vicinal surface, denoted by Δ 2 ( y ) ( y : distance along the step), is calculated based on the terrace-step-kink picture. For systems with only short-range step-step interactions, both the free-fermion approach and the capillary-wave approach are taken to derive the universal asymptotic behavior Δ 2 ( y )∼ A log y with A =(πρ) -2 ,where ρ is the step density. We present a general relation between Δ 2 ( y ) and the surface height-height correlation function, which connects the universal behavior to the universal Gaussian curvature jump at the facet edge. For the case with long-range (inverse-square) step-step interactions, we combine the exact solution of the Sutherland model with the capillary-wave theory. We successfully derive the non-universal amplitude A = A (ρ, g ) as a function of the coupling constant g .
TL;DR: In this paper, the authors used ensembles of high-resolution CDM simulations to investigate the shape and amplitude of the two-point correlation function of rich clusters and found that the amplitudes of the rich cluster correlation functions depend weakly on cluster richness.
Abstract: We use ensembles of high-resolution CDM simulations to investigate the shape and amplitude of the two-point correlation function of rich clusters. The standard scale-invariant CDM model with Ω=1 provides a poor description of the clustering measured from the APM rich cluster redshift survey, which is better fitted by models with more power at large scales. The amplitudes of the rich cluster correlation functions measured from our models depend weakly on cluster richness. Analytic calculations of the clustering of peaks in a Gaussian density field overestimate the amplitude of the N-body cluster correlation functions, but reproduce qualitatively the weak trend with cluster richness
TL;DR: In this article, the scattering intensity due to thermal fluctuations of the amphiphile density in microemulsion and sponge phases is calculated for a Ginzburg-Landau model with two scalar order parameters.
Abstract: The scattering intensity due to thermal fluctuations of the amphiphile density in microemulsion and sponge phases is calculated for a Ginzburg-Landau model with two scalar order parameters. The amphiphile correlations are found to be strongly influenced by the oil-water correlation function in the former and the water-water correlation function in the latter. We take these correlations to oscillate with wave vector k. Not only does this reproduce the known 1/q dependence of the scattering intensity for the small wave vector q, it also gives rise at q=2k to an experimentally oberved peak. The calculated scattering intensities agree very well with experimental results over the whole range of wave vectors.
TL;DR: In this paper, the authors compute the three-point temperature correlation function of the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) first-year sky maps to search for non-Gaussian temperature fluctuations.
Abstract: We compute the three-point temperature correlation function of the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) first-year sky maps to search for non-Gaussian temperature fluctuations The level of fluctuations seen in the computed correlation function are too large to be attributable solely to instrument noise However the fluctuations are consistent with the level expected to result from a superposition of istrument noise and sky signal arising from a Gaussian power-law model of initial fluctuations, with a quadrupole normalized amplitude of 17 micro K and a power-law spectral index n = 1 We place limits on the amplitude of intrinsic three-point correlations with a variety of predicted functional forms
TL;DR: It is demonstrated experimentally that the intensity correlation function with shift in the scattered wave vector or with identical shifts in both the incident and scattered wave vectors form Fourier transform pairs, respectively, with the intensity distribution on the output surface and the propagator between the input and output surfaces.
Abstract: We demonstrate experimentally that the intensity correlation function with shift in the scattered wave vector or with identical shifts in both the incident and scattered wave vectors form Fourier transform pairs, respectively, with the intensity distribution on the output surface and the propagator between the input and output surfaces. Measurements in samples with and without internal reflection are in excellent agreement with diffusion theory without adjustable parameters.
TL;DR: In this article, the authors present results for the triplet distribution function of hard spheres obtained in extensive molecular-dynamics simulations; the packing fractions range from 0.15 to 0.45.
Abstract: We present results for the triplet distribution function g(3)(r,s,t) of hard‐spheres obtained in extensive molecular‐dynamics simulations; the packing fractions we have investigated range from 0.15 to 0.45. The simulation data have been compared to results for g(3)(r,s,t) which we calculated via some recently proposed analytical and numerical methods; two of these methods are based on density‐functional theory and the Wertheim–Thiele solution of the Percus–Yevick equation; another method, proposed by Barrat, Hansen, and Pastore uses a factorization ansatz for the pair direct correlation function and the last approximation is based on a formal density expansion of g(3)(r,s,t), truncated after second order. Furthermore we compared, simulation results to data obtained by the ‘‘source‐particle method’’ (or PY3 method) proposed a few years ago by Attard. Attard’s method shows an extremely good agreement not only for general configurations, but in particular for particles at direct contact; this approximation h...
01 Jan 1994
TL;DR: In this article, the authors describe stochastic computer simulations of the local segmental dynamics of synthetic polymers, focusing on local dynamics in solution and issues of cooperativity in conformational transitions.
Abstract: This article describes stochastic computer simulations of the local segmental dynamics of synthetic polymers. Particular attention is given to local dynamics in solution. Related work involving experimental methods, analytical theory, and molecular dynamics simulations will also be discussed. An introduction to the concepts involved in stochastic simulations will be presented. Methods of characterizing local segmental dynamics will also be described. The main portion of the article describes various features of the simulated dynamics. The approximations inherent in stochastic approaches and their influence on the observed dynamics will be discussed. Issues of cooperativity in conformational transitions will be highlighted.
TL;DR: In this article, the authors determine the relaxational dynamics of the shape fluctuations of a fluid membrane in the vicinity of a substrate, including coupling between the local shape and the difference of the two monolayer densities as well as a lateral tension in the membrane.
Abstract: We determine the relaxational dynamics of the shape fluctuations of a fluid membrane in the vicinity of a substrate. Extending the "classical" description, we include the coupling between the local shape and the difference of the two monolayer densities as well as a lateral tension in the membrane. These extensions introduce additional length scales to the problem. The asymptotic behavior of the dispersion relation and the correlation functions can be understood from limiting cases in which either a free bilayer or a bound incompressible membrane is considered. In many cases, however, the relevant length scales do not separate very well, so that the full dispersion relation will be needed for the interpretation of experiments. It is shown that in addition to the damping due to bulk viscosity the dissipation due to friction between the monolayers is observable and indeed dominates the long-time behavior of the dynamical height correlation function for large wave vectors. As demonstrated with typical sets of parameters, the transition to this regime will be accessible by optical techniques only for weak adhesion and strong friction between the monolayers.
TL;DR: In this paper, the correlation function of the spin-1 chain with quadratic and biquadratic interactions was studied using the recently developed density matrix renormalization group approach.
Abstract: Using the recently developed density matrix renormalization group approach, we study the correlation function of the spin-1 chain with quadratic and biquadratic interactions. This allows us to define and calculate the periodicity of the ground state which differs markedly from that in the classical analogue. Combining our results with other studies, we predict three phases in the region where the quadratic and biquadratic terms are both positive.