On the correlation equalities for the random-bond Ising model

We obtain several equalities of the configurationally averaged spin correlation functions for the random-bond Ising model by means of a gauge transformation. These equalities are shown to be useful to find the exact results for the internal energy, an upper bound of the specific heat, the equality for the zero-field susceptibility and the zero-field spin glass susceptibility, and so on.     

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.     

Efficient algorithm for random-bond ising models in 2D

We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm computes the partition function and correlation functions at a single temperature on any planar network of N Ising spins in O(N;{3/2}) time or less. The method can handle continuous or discrete bond disorder and is especially efficient in the case of bond or site dilution, where it executes in O(NlnN) time near the percolation threshold. We demonstrate its feasibility on the ferromagnetic Ising model and the +/-J random-bond Ising model and discuss the regime of applicability in cases of full frustration such as the Ising antiferromagnet on a triangular lattice.     

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.     

Does quasi-long-range order in the two-dimensional XY model really survive weak random phase fluctuations?

Effective theories for random critical points are usually non-unitary, and thus may contain relevant operators with negative scaling dimensions. To study the consequences of the existence of negative-dimensional operators, we consider the random-bond XY model. It has been argued that the XY model on a square lattice, when weakly perturbed by random phases, has a quasi-long-range ordered phase (the random spin wave phase) at sufficiently low temperatures. We show that infinitely many relevant perturbations to the proposed critical action for the random spin wave phase were omitted in all previous treatments. The physical origin of these perturbations is intimately related to the existence of broadly distributed correlation functions. We find that those relevant perturbations do enter the Renormalization Group equations, and affect critical behavior. This raises the possibility that the random XY model has no quasi-long-range ordered phase and no Kosterlitz-Thouless (KT) phase transition.     

Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models

We report on large-scale Wang-Landau Monte Carlo simulations of the critical behavior of two spin models in two- (2d) and three-dimensions (3d), namely the 2d random-bond Ising model and the pure 3d Blume-Capel model at zero crystal-field coupling. The numerical data we obtain and the relevant finite-size scaling analysis provide clear answers regarding the universality aspects of both models. In particular, for the random-bond case of the 2d Ising model the theoretically predicted strong universality’s hypothesis is verified, whereas for the second-order regime of the Blume-Capel model, the expected d = 3 Ising universality is verified. Our study is facilitated by the combined use of the Wang-Landau algorithm and the critical energy subspace scheme, indicating that the proposed scheme is able to provide accurate results on the critical behavior of complex spin systems.     

Chiral ordering in the four-dimensional planar spin glass

The chiral glass behaviour of the nearest-neighbour random-bond XY spin glass in four dimensions is studied by Monte Carlo simulations. A chiral glass transition at T _cg = 0:90 ± 0:05 is found by a finite-size scaling analysis of the results. The associated chiral correlation-length exponent is estimated to be gv _cg = 0:6±0:1. Both values are very similar to those reported recently for the spin glass transition in this model. The results strongly suggest a simultaneous ordering of spin and chirality in four dimensions.     

Spin diffusion in anisotropic Heisenberg chains: S≥1/2

In this paper, we investigate spin diffusion in Heisenberg chains with uniaxial nearest-neighbor interactions. The approach followed is based on an analysis of the infinite-temperature longitudinal spin density and spin current correlation functions. For S=1/2, exact results are presented for the time-dependent correlation functions in the XY limit. Away from this limit, the second and fourth moments of the Fourier transform of the spin density correlation function provide information about spin dynamics for arbitrary values of the spin. The moments are used in an assessment of the accuracy of the Gaussian approximation for the spin diffusion constant for S=1/2. The general behavior of the Gaussian approximation when S>1/2 is discussed, and numerical results for the spin diffusion constant are presented for S=1/2, 1, 3/2, 2 and in the classical limit. A moment-based criterion for the boundary in reciprocal space between diffusive and non-diffusive dynamics that applies to arbitrary values of the spin is presented.     

Spin-Dependent Forces and Current Quark Masses

The J = (3/2) , J = 1/2 Nucleon mass difference shows the quark energies can be spin dependent. It is natural to expect that the quark wave functions also depend on spin. A spin-dependent quark force is fitted to the proton and neutron magnetic moments, axial charge, and spin content using a (1/2⁺)³ configuration for the quarks and assuming only zero mass u and d quarks are in the nucleon. In the octet, such spin-dependent forces lead to different wave functions for quarks with spin parallel or antiparallel to the nucleon spin. The eigen-energy of this potential is 0.15 GeV higher for quark spin parallel than for the quark spin antiparallel to the proton spin. This potential predicts a single quark energy of 0.37 GeV for mass-less quarks in the Delta. Assuming the quark forces are flavor independent, this potential predicts magnetic moments of a bound strange quark to be very close to those determined empirically from the octet magnetic moments.     

Nuclear effects in the F3 structure function for finite and asymptotic Q

We study nuclear effects in the structure function F₃ which describes the parity violating part of the charged-current neuitrino nucleon deep inelastic scattering. Starting from a covariant approach we derive a factorized expression for the nuclear structure function in terms of the nuclear spectral function and off-shell nucleon structure functions valid for arbitrary momentum transfer Q and in the limit of weak nuclear binding, i.e. when a nucleus can be treated as a non-relativistic system. We develop a systematic expansion of nuclear structure functions in terms of a Q⁻² series caused by nuclear effects (“nuclear twist” series). Basing ourselves on this expansion we calculate nuclear corrections to the Gross-Llewellyn-Smith sum rule as well as to higher moments of F₃. We show that corrections to the GLS sum rule due to nuclear effects cancel out in the Bjorken limit and calculate the corresponding Q⁻² correction. Special attention is paid to the discussion of the off-shell effects in the structure functions. A sizable impact of these effects both on the Q² and x dependence of nuclear structure functions is found.     

Nonextensive entropy and the non-Gaussian distribution of magnetization in two-dimensional spin ice

The statistical properties of the magnetization of the finite clusters of two-dimensional spin ice have been investigated. It has been shown by Monte Carlo simulations that the short-range ice rules in two dimensions lead to long-range correlations, which decay by a power law with distance. The long-range correlations, in turn, cause the nonextensivity of entropy and inapplicability of the central limit theorem for the magnetization. The behavior of the moments and distribution function of the magnetization with the cluster size disagrees with the theoretical predictions of the dipolar behavior of the correlation functions in two-dimensional spin ice.     

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.     

Transport coefficients in Heisenberg paramagnets

The Heisenberg model is discussed in the paramagnetic region, using the method of moments in the spectral representation of spin correlation functions. We discuss the validity of Green's function decoupling approximations and derive expressions for the spin diffusion and thermal conductivity of a simple cubic lattice and linear chain. The results of the calculations are in qualitative agreement with previous work.     

Metallic spin-liquid behavior of the geometrically frustrated Kondo lattice

Strongly frustrated magnetism of the metallic pyrochlore oxide Pr2Ir2O7 has been revealed by single crystal study. While Pr 4f moments have an antiferromagnetic RKKY interaction energy scale of /T*/ = 20 K mediated by Ir 5d-conduction electrons, no magnetic long-range order is found except for partial spin freezing at 120 mK. Instead, the Kondo effect, including a lnT dependence in the resistivity, emerges and leads to a partial screening of the moments below /T*/. Our results indicate that the underscreened moments show spin-liquid behavior below a renormalized correlation scale of 1.7 K.     

Magnetic Properties of Spin-1/2 Quantum Heisenberg Ferromagnet with Spatially Anisotropy

The spin-1/2 quantum Heisenberg ferromagnet with anisotropic spin exchange interactions in three dimensions are investigated by means of the Green's function method. In the Tyablikov approximation, the correlation functions, the magnetization, and the susceptibilities are computed. The magnetic properties of this model are found to be dependent of anisotropy.     

Linking total cross sections for hard and soft processes through analyticity in Q and sum rules

Using analyticity of the virtual Compton scattering amplitude in Q² sum rules are derived relating meson-nucleon total cross-sections with certain integrals over the large Q² and x0 part of nucleon structure functions. Of preliminary quantitative analysis of the sum rules for both singlet and non-singlet amplitudes is presented. For the singlet amplitude the sum rules relate, in particular, the rise of sea-quark distributions implied by perturbative QCD and the increase of total meson-proton cross sections with energy. Quantitatively, however, nonunitary leading log Q² results for the former give a too rapid increase of the latter.     

On the theory of NMR spin echoes in solids

A general expression in terms of two-time correlation functions is derived for the spin echo responses to 90°-τ-β⁰_φ pulse sequences of quadrupolar spins coupled through dipolar interactions. The second moments of the correlation function are calculated for a system of spin one nuclei and shown to be in accordance with the experimental observations. Furthermore, results are presented for the fourth moments.     

Hubbard模型的局域方法近似

本文基于同一格点的电子相关和最近邻格点间的电荷相关及自旋相关,把局域方法的级数展开用于Hubbard模型。和通常的二阶计算不同,我们在计算中保留了项。比较这两种不同计算方法所得到的结果,发现在U较大时,项对顺磁相的相关能、基态能量、局域磁矩和由局域磁矩引起的反铁磁极化均有不可忽略的修正。要准确计及电子相关效应,还需通过作更高阶展开,以考察级数的收敛性。 关键词：     

High-temperature dynamics of the anisotropic spin-1/2 square lattice Heisenberg model studied by moment methods

The spin dynamics of the anisotropic spin-1/2 nearest-neighbour Heisenberg model (XYZ model) on a plane square lattice is studied at infinite temperature. Low-order coefficients of the short-time expansions for spin-spin correlation functions are calculated. The necessary commutator algebra may be performed by a computer. The series obtained for the spin correlation function are the longest ones available up to now. The series coefficients are used to construct rigorous upper and lower bounds to autocorrelation functions and near-neighbour correlation functions.     

一维自旋轨道模型中自旋-轨道能隙产生机理分析

讨论考虑洪特耦合的两带赫伯德模型得到的一维自旋轨道模型中自旋-轨道能隙的产生.运用SU(4)赝费米子表象下的平均场理论,计算求得价键序参数、准粒子激发谱能隙和自旋、轨道密度-密度关联函数随系统耦合参数变化的结果.随洪特耦合相互作用由零开始增强,系统激发谱能隙逐渐打开,并且系统在参数取值为J₁/J₂=1/3处由具有阻错的无序状态相变到自旋铁磁有序和轨道反铁磁有序的状态.