High-temperature dynamics of the anisotropic Heisenberg chain studied by moment methods

The dynamics of the anisotropic spin-1/2 nearest-neighbour Heisenberg chain is studied at infinite temperature. Low-order coefficients of the short-time expansions are computed for spin-spin and energy-density-energy-density correlation functions for cyclical as well as for open-ended chains. The commutator algebra necessary to generate these coefficients may be performed by a computer. The series obtained for the spin correlation function (up to ordert ¹⁴ for a bulk spin and up to ordert ¹⁸ for a boundary spin) and for the energy density correlation function are the longest ones available up to now. The coefficients are used to construct rigorous upper and lower bounds to autocorrelation functions and near-neighbour correlation functions.     

Magnetization and spin-spin energy diffusion in the XY model: a diagrammatic approach

It is shown that the diagrammatic cluster expansion technique for equilibrium averages of spin operators may be straightforwardly extended to the calculation of time-dependent correlation functions of spin operators. We use this technique to calculate exactly the first two non-vanishing moments of the spin-spin and energy-energy correlation functions of the XY model with arbitrary couplings, in the long-wavelength, infinite temperature limit appropriate for spin diffusion. These moments are then used to estimate the magnetization and spin-spin energy diffusion coefficients of the model using a phenomenological theory of Redfield. Qualitative agreement is obtained with recent experiments measuring diffusion of dipolar energy in calcium fluoride.     

Manifestly finite perturbation theory for the short-distance expansion of correlation functions in the two-dimensional Ising model

We review and apply the recently proposed formalism for the study of the theory space of euclidean quantum field theories based on the variational formula to the analysis of the scaling limit of the two-dimensional massive Ising model. An extension of the first-order variational formula to higher orders provides a manifestly finite scheme for the perturbative calculation of the operator product coefficients to any order in parameters. A perturbative expansion of the correlation functions follows. We implement this scheme for a systematic study of correlation functions involving two spin operators. We show how the necessary non-trivial integrals can be calculated. As two concrete examples we explicitly calculate the short-distance expansion of the spin-spin correlation function to third order and the spin-spin-energy-density correlation function to first order in the mass. We also comment on how our results may be applied to perturbations of non-trivial fixed points corresponding to other unitary minimal models.     

New effective-field theory with correlations; application to disordered magnets

The Ising model of spin 1/2 with nearest-neighbour interaction is investigated. Within the effective-field theory introduced by Honmura and Kaneyoshi, a new type of decoupling approximation is introduced for treating the multispin correlation functions. The critical temperature, the spontaneous magnetization, and the two-site spin c correlation function are calculated for a two- (or three-) dimensional lattice. The present formalism yields results better than those of Bethe-Peierls approximation and is extended to disordered magnets. The thermodynamical quantities of quenched random-bond magnets, such as magnetization, susceptibility and so on, are studied, We find that in particular the twosite spin correlation functions of the disordered magnets exhibit some interesting behavior.     

Order and disorder lines in systems with competing interactions. III. Exact results from stochastic crystal growth

The methods presented in the first two articles of this series are simplified and generalized by growing stationary stochastic crystals from a given Ansatz layer. On the disorder trajectory the free energy, correlation functions, and multicritical points are calculated explicitly for a large class of models with competing interactions, including the staggered eight-vertex model, the general sixteen-vertex model, theq-state Potts model on a triangular lattice, a generalZ(q) model, and restricted spin glass models in two dimensions.     

Gaussian bounds for correlations in lattice spin systems

In quite generalN-component ferromagnetic spin systems, it is proved that an arbitrary correlation function is bounded by the corresponding correlation function of a Gaussian model. The bound is useful for the analysis of high-temperature behavior of the system. Similar bounds for truncated correlation functions are also obtained for a class of single-component spin systems.     

Upper bounds for ground-state correlation functions in the Hubbard model

We present rigorous bounds on the ground-state spin and charge correlation functions of the single-band Hubbard model defined on a bipartite lattice. In the attractive case, the spin correlation function is bounded from above by a quantity depending only on the value of the Coulomb interaction. A similar result is obtained in the half-filled repulsive model when the charge and the on-site pairing correlation functions are considered. The present results imply that the related susceptibilities never diverge and the absence of corresponding long-range orders.     

Spin-orbit interactions in semiconductor superlattice

The purpose of this paper is to theoretically investigate the spin-orbit interactions of common semiconductor superlattices. Spin splitting and spin-orbit interaction coefficients are calculated based on interactions between the interface-related-Rashba effect and Dresselhaus effect. Semiconductor superlattice shows a series of specific characteristics in spin splitting as follows. The spin splitting of the superlattice structure is greater than that of a single quantum well, contributing to significant spin polarization, spin filtering, and convenient manipulation of spintronic devices. The spin splitting of some superlattice structures does not change with variation of the size of some constituent quantum wells, reducing the requirements for accuracy in the size of quantum wells. The total spin splitting of lower sub-levels of some superlattice can be designed to be zero, realizing a persistent spin helix effect and long spin relaxation time, however, the total spin splitting of higher sub-levels is still appreciable, contributing to desirable spin polarization. These results demonstrate that one superlattice structure can realize two functions, acting as a spin field effect transistor and a spin filter.     

Nonlinear identification of NMR spin systems by adaptive filtering

In this paper, we present two new methods for identifying NMR spin systems. These methods are based on nonlinear adaptive filtering. The spin system is assumed to be time-invariant with memory. The first method uses a truncated discrete Volterra series to describe the nonlinear relationship between excitation (input) and system response (output). First-, second-, and third-order kernels of this series are estimated employing the least mean square (LMS) algorithm. Three parallel filters can then model the NMR spin system so that its output is no more than simple sum of three convolution products between combinations of the input signal and filters coefficients. It is also shown that the contribution of the Volterra second-order term to the total system response is neglected compared with the contributions of the first- and the third-order terms. In the second identification method, the output signal is related to the input signal through a recursive nonlinear difference equation with constant coefficients. The LMS algorithm is used again to estimate the equation coefficients. The two methods are validated with a simulated NMR system model based on Bloch equations. The results and the performances of these methods are analyzed and compared. It is shown that our methods permit a simple identification of NMR spin systems. The field of applications of this study is promising in the optimization of NMR signal detection, especially in the cases of low signal-to-noise ratios where optimum signal filtering and analysis must be performed.     

Correlation functions in the multiple Ising model coupled to gravity

The model of p Ising spins coupled to 2d gravity, in the form of a sum over planar φ³ graphs, is studied and in particular the two-point and spin-spin correlation functions are considered. We first solve a toy model in which only a partial summation over spin configurations is performed and, using a modified geodesic distance, various correlation functions are determined. The two-point function has a diverging length scale associated with it. The critical exponents are calculated and it is shown that all the standard scaling relations apply. Next the full model is studied, in which all spin configurations are included. Many of the considerations for the toy model apply for the full model, which also has a diverging geometric correlation length associated with the transition to a branched polymer phase. Using a transfer function we show that the two-point and spin-spin correlation functions decay exponentially with distance. Finally, by assuming various scaling relations, we make a prediction for the critical exponents at the transition between the magnetized and branched polymer phases in the full model.     

THE APPLICATIONS OF NUCLEAR SPIN RELAXATION TO POLYMER DYNAMICS AND INTERMOLECULAR INTERACTIONS

The correlation functions of the side - groups and side ?chains of polymers are obtained for nuclear spin relaxation if the segmental motion of the polymers is described by VJGM model, these functions are derived from unequal two ?side and three -site jump internal rotation, diffusion internal rotation, restricted internal rotation and multiple internal rotation. The corresponding spectral density functions are also given, and these functions are used to interpret the nuclear spin relaxation data of the side-groups of some polymers. The average spectral density functions of side-groups are derived under the magic angle spinning, the correlation times and diffusion coefficients of the side-groups of crosslinked poly (methyl methacry-latcs) and solid poly(vinylbutyral) are obtained by using these average spectral density functions. The multiphase structures of nylon 6, poly (ethylenc glycol) and its complexes are investigated with cross ?polarization and magic angle spinning techniques.Three methods using     

Soliton contribution to correlations in a system of coupled chains

A model representing a two- or a three-dimensional array of classical harmonic chains withnonlinear coupling between them is investigated. Physically real systems to which this model applies are discussed. The model exhibits soliton-like nonlinear modes. The influence of these nonlinear modes on the static and the dynamic correlation functions is calculated by generalizing techniques developed for strictly one-dimensional systems. In the static correlation functions these modes lead to minor quantitative changes only. In certain dynamic correlation functions, however, a central peak is found to occur due to the nonlinear modes. The total weight and the width of this peak are calculated for a real spin system.     

Spin correlations in a non-frustrated one-dimensional spin system,and formation of the ground state as a model of protein folding

The properties of correlation functions between spins in a specific spin model with no frustration, and with high frustration are compared. It was already confirmed that the ground state formation of our no frustration model showed two-state Arrhenius-like kinetics, such as observed in protein folding. In this paper, we present that the correlation functions of the non-frustration system are characterized by spin motions of the lowest eigenvalue mode, defined by the interspin interactions near the transition temperature. The Arrhenius kinetics are regarded as the transition between this and the ground states, and thus our result denotes the implication to the protein folding mechanism.     

Spinon and <Emphasis Type="Italic">η</Emphasis>-spinon correlation functions of the Hubbard chain

We calculate real-space static correlation functions of spin and charge degrees of freedom of the one-dimensional Hubbard model that are described by operators related to singly occupied sites with spin up or spin down (spinons) and unoccupied or doubly occupied sites (η-spinons). The spatial decay of their correlation functions is determined using density matrix renormalization group results. The nature and spatial extent of the correlations between two sites on the Hubbard chain is studied using the eigenstates and eigenvalues of the two-site reduced density matrix. The results show that the spinon-spinon correlation functions decay algebraically and the η-spinon correlation functions decay exponentially, both in the half-filling and metallic phases. The results provide evidence that these degrees of freedom are organized in boundstates in the interacting system.     

QCD resummation for single spin asymmetries

We study the transverse momentum dependent factorization for single spin asymmetries in Drell-Yan and semi-inclusive deep inelastic scattering processes at one-loop order. The next-to-leading order hard factors are calculated in the Ji-Ma-Yuan factorization scheme. We further derive the QCD resummation formalisms for these observables following the Collins-Soper-Sterman method. The results are expressed in terms of the collinear correlation functions from initial and/or final state hadrons coupled with the Sudakov form factor containing all order soft-gluon resummation effects. The scheme-independent coefficients are calculated up to one-loop order.     

Correlated correlation functions in random-bond ferromagnets

The two-dimensional random-bond Q-state Potts model is studied for Q near 2 via the perturbative renormalisation group to one loop. It is shown that weak disorder induces cross-correlations between the quenched-averages of moments of the two-point spin/spin and energy/energy correlation functions, which should be observable numerically in specific linear combinations of various quenched correlation functions. The random-bond Ising model in (2+ε) dimensions is similarly treated. As a byproduct, a simple method for deriving the scaling dimensions of all moments of the local energy operator is presented.     

A renormalization group analysis of correlation function series expansions

A new method, inspired by renormalization group ideas, is proposed for extracting information on critical behaviour from series expansions of correlation functions. For the two-dimensional spin $\text{1}\text{2}$XY model, the results suggest the existence of a line of critical points.     

Broad peak in the dx2-y2 superconducting correlation length as a function of hole concentration in the two-dimensional t-J model

We have calculated high temperature series to 12th order in inverse temperature for singlet superconducting correlation functions of the 2D t-J model with s, dx2-y2, and dxy symmetry pairs. Our calculations differ from previous work by removing disconnected pieces from the original four-point correlator and by treating the resulting pairing correlator as a matrix. We find the correlation length for dx2-y2 pairing grows significantly with decreasing temperature and develops a broad peak as a function of doping around delta=0.25 for T/J=0.25 at J/t=0.4. The correlation lengths for s and dxy symmetry remain small and do not display peaks. Antiferromagnetic spin correlations at low doping act to suppress the dx2-y2 and dxy superconducting correlation lengths.     

Correlation inequalities in quantum statistical mechanics and their application in the Kondo problem

We consider a large class of models which share the essential features of the Kondo model. Bounds on the susceptibility of the impurity spin are derived as consequences of general inequalities for quantum correlation functions. We also obtain bounds for the spin polarization in the presence of an external field.