Existence and renormalization of the Sine-Gordon field theory in all dimensions

The Euclidean field theory of the Sine-Gordon model (SG) is investigated by using methods of statistical physics. The SG model is shown to be the continuum limit of the ferromagnetic Harmonic Rotator model (HR) which itself is equivalent to a classical Coulomb plasma of unit charges on a lattice. Using our recent results for the latter models in all Euclidean dimensionsD we determine the existence of the SG field theory in terms of the HR parameters, temperaturet and magnetic fieldB. The following results are derived: 1. InD=1 the SG exists neart=B=0; the quantum theory in zero space dimensions is just the Mathieu equation as Schrödinger equation. 2. ForD>2 the SG field theory exists for allt nearB=0. The theory is actually constructed and is equivalent to a free massive scalar theory. 3. In the most interesting case ofD=2 the SG field theory exists for allt<t=8 nearB=0, it does not exist fortt. All necessary renormalizations are performed and all necessary subtractions are obtained in closed form which proves that the theory is superrenormalizable when it exists. We also discuss the relations between the structure of the particle spectrum of the SG, the phase transitions of the HR, and the binding properties of the classical Coulomb charges.     

Spin-glass in the spinel-type CuCrTiS4

It is difficult to find a typical compound to understand the spin-glass (SG). Only a few model compounds for the SG have been investigated; Fe_0.50Mn_0.50TiO₃ as a short-range interacting three-dimensional (3D) Ising SG, Dy_0.103Y_0.897Ru₂Si₂ as a long-range 3D Ising SG, and AgMn as a long-range 3D Heisenberg SG. A spinel-type compound CuCrTiS₄ will be provided in this study as a realistic candidate for a short-range interacting 3D Heisenberg SG. This CuCrTiS₄ can cause a SG phase below T _g?=?7.91?K, which is obtained by a random non-magnetic 50% substitution of Ti for Cr on B-sites in the ferromagnetic mother spinel CuCr₂S₄. The localized magnetic moment of CuCrTiS₄ comes from Cr³⁺ with S?=?3/2, where a valence state of Cu⁺Cr³⁺Ti⁴⁺S₄ ^2? is built up. Experimental data will be focused only on the static properties of dc magnetization M(T) under various magnetic fields, without any dynamical magnetic feature. The spin-glass phase transition T _g is well defined at low field, nevertheless hardly in higher fields than approximately 40 Oe. An appearance of the field dependence of M(T) of CuCrTiS₄ is similar to that of Fe_0.50Mn_0.50TiO₃ with the short-range Ising SG, and also these of AgMn and CuMn with the long-range interacting Heisenberg SGs. This general nature in M(T) seems to originate from the common mechanism under magnetic fields for all the spin-glasses.     

Second order phase transition in two dimensional sine-Gordon field theory—Lattice model

Two dimensional sine-Gordon (SG) field theory on a lattice is studied using the single-site basis variational method of Drell and others. The nature of the phase transition associated with the spontaneous symmetry breakdown in a SG field system is clarified to be of second order. A generalisation is offered for a SG-type field theory in two dimensions with a potential of the from [cos ⁿ (√λ/m)ϕ−1].     

Fermionic Ising glasses with BCS pairing interaction. Tricritical behaviour

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This model is obtained by using perturbation theory to trace out the conduction electrons degrees of freedom in conventional superconducting alloys. The model is formulated in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann fields and it reduces to a single site problem that can be solved within the static approximation with a replica symmetric ansatz. We argue that this is a valid procedure for values of temperature above the de Almeida-Thouless instability line. The phase diagram in the T-g plane, where g is the strength of the pairing interaction, for fixed variance J ² /N of the random couplings J_ij, exhibits three regions: a normal paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase where there is formation of local pairs.The NP and PAIR phases are separated by a second order transition line g=g _c (T) that ends at a tricritical point T ₃ =0.9807J, g ₃ =5,8843J, from where it becomes a first order transition line that meets the line of second order transitions at T _c =0.9570J that separates the NP and the SG phases. For T<T _c the SG phase is separated from the PAIR phase by a line of first order transitions. These results agree qualitatively with experimental data in . Received 14 May 1998     

Spin glass and antiferromagnetism in Kondo-lattice disordered system

The competition between spin glass (SG), antiferromagnetism (AF) and Kondo effect is studied here in a model which consists of two Kondo sublattices with a Gaussian random interaction between spins in different sublattices with an antiferromagnetic mean J ₀ and standard deviation J. In the present approach there is no hopping of the conduction electrons between the sublattices and only spins in different sublattices can interact. The problem is formulated in the path integral formalism where the spin operators are expressed as bilinear combinations of Grassmann fields which can be solved at mean field level within the static approximation and the replica symmetry ansatz. The obtained phase diagram shows the sequence of phases SG, AF and Kondo state for increasing Kondo coupling. This sequence agrees qualitatively with experimental data of the Ce₂Au_1-x Co _x Si₃ compound.Received: 9 April 2003, Published online: 9 September 2003PACS: 05.50.+q Lattice theory and statistics; Ising problems - 64.60.Cn Order disorder transformations; statistical mechanics of model systems     

SYBR Green I: Fluorescence Properties and Interaction with DNA

In this study, we have investigated the fluorescence properties of SYBR Green I (SG) dye and its interaction with double-stranded DNA (dsDNA). SG/dsDNA complexes were studied using various spectroscopic techniques, including fluorescence resonance energy transfer and time-resolved fluorescence techniques. It is shown that SG quenching in the free state has an intrinsic intramolecular origin; thus, the observed >1,000-fold SG fluorescence enhancement in complex with DNA can be explained by a dampening of its intra-molecular motions. Analysis of the obtained SG/DNA binding isotherms in solutions of different ionic strength and of SG/DNA association in the presence of a DNA minor groove binder, Hoechst 33258, revealed multiple modes of interaction of SG inner groups with DNA. In addition to interaction within the DNA minor groove, both intercalation between base pairs and stabilization of the electrostatic SG/DNA complex contributed to increased SG affinity to double-stranded DNA. We show that both fluorescence and the excited state lifetime of SG dramatically increase in viscous solvents, demonstrating an approximate 200-fold enhancement in 100?% glycerol, compared to water, which also makes SG a prospective fluorescent viscosity probe. A proposed structural model of the SG/DNA complex is compared and discussed with results recently reported for the closely related PicoGreen chromophore.     

Mean-field theories of spin glasses

Different kinds of mean-field theories (MFT) of spin glasses (SG) are reviewed. A brief introductory review of major experimental results, which have to be explained theoretically, is presented in the beginning. Marshall-Klein-Brout type random local field theories are described qualitatively. Edwards-Anderson MFT of SG transition is introduced after defining the various relevant order parameters. Almost all the static and dynamic approaches to the solution of the Sherrington-Kirkpatrick model are reviewed in detail. The existence of mixed phase(s) in the MFT of vector SG is examined critically in the light of recent theories and experiments. The existence of macroscopic anisotropy energy in SG and their microscopic origin are mentioned. The upper and lower critical dimensionalities obtained by different authors are enlisted. The concept of frustration and its deeper connection with other branches of human knowledge are indicated. Nonlinear susceptibilities, spin wave and relaxational modes in SG are also reviewed. The two-level-system picture of SG, its physical basis and important consequences are presented. The Tholence-Tournier-Wohlfarth phenomenological cluster model of SG is discussed with a stress on the role of measurement time. SG transition has been described as percolation and localization-delocalization problems. Some special features of the local field distribution in SG are mentioned. Some results of computer simulation on the various models of SG are summarized. The theories of the transport properties of SG are enlisted. Recent trends in the theory of SG are indicated at the end.     

A Hamiltonian approach to the strong gravity limit

The Hamiltonian for general relativity is examined in the strong gravity (SG) limitG . In this limit a perfect fluid moves irrotationally along geodesics. An appropriate SG limit for the scalar field is developed such that the energy density has a limit. The solutions in this limit, which were previously known, are shown to come out simply and directly. A classification of the trace-free part of the momentum is given in the Appendix.     

On excess magnetoconductivity of a superconductive glass

The behaviour of an excess conductivity in the presence of a magnetic field is studied via the superconductive glass (SG) model. The paper predicts a crossover between two- and three-dimensional behaviours of paraconductivity. It is shown that for temperatures well aboveT _c (when a typical distance between grains is larger than the correlation length) a two-dimensional analog of the Aslamazov-Larkin law is realized, and in the region nearT _c paraconductivity reduces to a three-dimensional form of theXY-like model of a granular superconductor. The obtained results are in qualitative agreement with the data for high-T _c superconductors (HTS).     

Stability conditions for fermionic Ising spin-glass models in the presence of a transverse field

The stability of a spin-glass (SG) phase is analyzed in detail for a fermionic Ising SG (FISG) model in the presence of a magnetic transverse field Γ. The fermionic path integral formalism, replica method and static approach have been used to obtain the thermodynamic potential within one step replica symmetry breaking ansatz. The replica symmetry (RS) results show that the SG phase is always unstable against the replicon. Moreover, the two other eigenvalues λ_± of the Hessian matrix (related to the diagonal elements of the replica matrix) can indicate an additional instability to the SG phase, which enhances when Γ is increased. Therefore, this result suggests that the study of the replicon cannot be enough to guarantee the RS stability in the present quantum FISG model, especially near the quantum critical point. In particular, the FISG model allows changing the occupation number of sites, so one can get a first order transition when the chemical potential exceeds a certain value. In this region, the replicon and the λ_± indicate instability problems for the SG solution close to all ranges of a first order boundary.     

甘蔗清糖浆锤度近红外光谱分析的模型优化

采用偏最小二乘法(PLS)和光谱Savitzky-Golay(SG)平滑方法,建立甘蔗清糖浆锤度近红外光谱分析的优化模型。基于最优单波长模型预测效果划分定标集和预测集。全谱(400—2500nm)经过SG平滑处理后用PLS方法建模。建立计算机算法平台,把483种SG平滑模式和1—40的PLS因子数任意组合分别建立PLS模型,根据预测效果选出最优模型,最优模型的SG平滑模式为二阶导数平滑、4、5次多项式类型、43平滑点数,PLS因子数为13,预测均方根偏差(RMSEP)、相对预测均方根偏差(RRMSEP)和预测相关系数(rP)分别为0.433%、0.69%和0.978。预测精度很高,并且大幅度优于未做SG平滑处理直接PLS建模的预测效果。从而表明,SG平滑模式和PLS因子数的联合大范围筛选能够有效地应用于近红外光谱分析的模型优选。     

Revisiting Spin Glasses: Impact of Spin-Spin Interaction Range

A study of the physical properties of spin glass systems (SG) is carried out within the Monte Carlo technique. The studied systems are the “classic” CuMn and AuFe metallic alloys, where the RKKY interaction is used as a model for the interaction among the magnetic (Mn, Fe) atoms. A careful discussion about the approach to the equilibrium is addressed. By introducing a cutoff radius in the range on the spin-spin interaction, the results show the influence of this range on the spin-glass behavior of the alloys, where the SG behavior is only observed when the full (long range) RKKY is taken into account, specially for low concentrations x <?0.05.     

Vis-NIR光谱模式识别结合SG平滑用于转基因甘蔗育种筛查

以Savitzky-Golay (SG)平滑筛选,主成分分析(PCA)分别结合有监督的线性判别分析(LDA)、无监督的系统聚类分析(HCA),应用于转基因甘蔗育种筛查的可见-近红外(Vis-NIR)无损检测。提出兼顾随机性、稳定性的定标、预测、检验框架;取田间种植处于伸长期甘蔗叶样品456个,具有Bt基因和Bar基因的转基因样品(阳)306个,非转基因样品(阴)150个;随机选取156个为检验集(阴性50、阳性106),余下为建模集(阴性100、阳性200,共300),建模集再随机划分为定标集(阴性50、阳性100,共150)、预测集(阴性50、阳性100,共150)共50次;扩充SG平滑点数,同时删除绝对值偏小的高阶导数模式,共264个平滑模式用于模型筛选;采用前3个主成分两两组合,再根据模型效果选出最优主成分组合;基于所有定标、预测集划分和SG平滑模式,建立SG-PCA-LDA和SG-PCA-HCA模型,根据平均预测效果优选参数,使模型具有稳定性;最后用检验集进行模型检验。经SG平滑后,PCA-LDA和PCA-HCA的建模精度、稳定性均显著改善;最优SG-PCA-LDA模型阳性、阴性样品检验识别率分别达到94.3%和96.0%;最优SG-PCA-HCA模型阳性、阴性样品检验识别率分别达到92.5%和98.0%。结果表明：Vis-NIR光谱模式识别结合SG平滑可用于转基因甘蔗叶的准确识别,提供了一种简便的转基因甘蔗育种筛查方法。     

Correlation functions of the 1-D coulomb gas,solitons and the 1-D Fermi gas

We study various correlation functions of the classical one-dimensional two component Coulomb gas (1-D CG). As a first example the dielectric function _q is considered. Explicit expressions for the first two terms of the long-wavelength expansion of _q ^-1 are rigorously derived by extending the method of Edwards and Lenard. On account of the equivalence between the 1-D CG and the sine-Gordon (SG) model _q can also be viewed as a correlation function of the SG field and the effects of small amplitude oscillations and of solitons can be traced in _q . We show that the nonmetallic nature of the 1-D CG is solely attributable to solitons. A similar analysis is carried out for other correlation functions. We establish a relation between these correlation functions and certain response functions of a one-dimensional Fermi gas by exploiting the known equivalence between the backward-scattering model of the Fermi gas and a 2-D CG on the surface of a cylinder and by investigating the conditions under which this 2-D CG can be considered one-dimensional.     

FTIR/ATR光谱应用于甘蔗糖蜜锤度的快速测定

采用FTIR/ATR光谱,偏最小二乘法(PLS)和Savitzky-Golay(SG)平滑方法建立甘蔗糖蜜锤度的快速测定方法和光谱分析的优化模型。基于全谱4500—600cm-1,利用计算机算法平台,把483种SG平滑模式和1—40的PLS因子数任意组合分别建立PLS模型。根据预测效果,最优模型为原谱平滑,2、3次多项式类型,45平滑点数,PLS因子数为6,预测均方根偏差(RMSEP)、预测相关系数(rp)和相对预测均方根偏差(RRMSEP)分别为0.978%、0.902%和1.05%,预测精度很高,并且大幅度优于未做SG平滑处理直接用PLS建模的预测效果。从而表明,FTIR/ATR光谱能够应用于甘蔗糖蜜锤度的快速准确测定,SG平滑模式和PLS因子数的联合大范围筛选能够有效地应用于FTIR/ATR光谱分析的模型优选。     

柑橘叶片叶绿素含量拉曼光谱定量分析方法研究

柑橘叶片叶绿素含量的准确检测对柑橘营养状况和生长态势具有极其重要的意义。研究了快速无损诊断柑橘叶片中叶绿素含量的方法,以期为拉曼光谱检测技术用于柑橘叶片叶绿素含量检测提供参考。采集不同冠层高度和不同地理分布的柑橘叶片120片,拭去叶片表面的灰尘,用去离子水对其清洗、晾干装入密封袋中并用标签分类标注。然后对柑橘叶片进行拉曼光谱采集,参数设置如下：分辨率为3 cm-1,积分时间为15 s;激光功率为50 mW。分别采用BaselineWavelet、迭代限制最小二乘（IRLS）和不对称最小二乘(ALS)三种算法对柑橘叶片的拉曼光谱背景进行扣除,使用偏最小二乘（PLS）方法建立定量模型;四种光谱预处理方法归一化(Normalization),Savitzky-Golay卷积平滑(SG smoothing, SG平滑)、多元散射校正(MSC)和Savitzky-Golay一阶导数(SG 1st Der)对扣除背景后的光谱进行进一步的优化处理。结果表明：采用原始光谱、BaselineWavelet、IRLS、ALS背景扣除处理后的光谱建立PLS模型,模型的相关系数r分别为0.858,0.828,0.885和0.862,交互验证均方根误差(RMSECV)分别为5.392,5.870,4.934和5.336,最佳因子数分别为8,3,8和8;IRLS背景扣除处理后的PLS模型的RMSECV最小,相关系数最高,建模效果最好。分别采用SG平滑、归一化、MSC和SG 1st Der预处理方法对IRLS背景扣除后光谱进行预处理并建立PLS模型,结果表明：IRLS光谱及其结合SG平滑、归一化、MSC和SG 1st Der四种预处理方法的PLS模型的R分别为0.885,0.897,0.852,0.863和0.888,RMSECV分别为4.934,4.715,5.595,5.182和4.962;最佳因子数分别为8,8,8,8和5;IRLS-SG平滑后PLS模型的RMSECV最小,模型效果最优。对IRLS-SG平滑预处理后的PLS模型展开验证,预测相关系数r为0.844,预测均方根误差(RMSEP)为5.29,预测精确度较高。采用拉曼光谱结合三种光谱背景扣除方法和四种预处理方法对柑橘叶片叶绿素含量进行定量分析表明：采用IRLS背景扣除结合SG平滑预处理后的PLS模型最优,建模集r为0.897,RMSECV为4.715;预测集r为0.844,RMSEP为5.29,预测精度较高。拉曼光谱结合背景扣除方法可以为柑橘叶片叶绿素含量的定量分析提供一种快速简便的分析方法。     

Fermionic van Hemmen spin glass model with a transverse field

In the present work it is studied the fermionic van Hemmen model for the spin glass (SG) with a transverse magnetic field Γ. In this model, the spin operators are written as a bilinear combination of fermionic operators, which allows the analysis of the interplay between charge and spin fluctuations in the presence of a quantum spin flipping mechanism given by Γ. The problem is expressed in the fermionic path integral formalism. As results, magnetic phase diagrams of temperature versus the ferromagnetic interaction are obtained for several values of chemical potential μ and Γ. The Γ field suppresses the magnetic orders. The increase of μ alters the average occupation per site that affects the magnetic phases. For instance, the SG and the mixed SG+ferromagnetic phases are also suppressed by μ. In addition, μ can change the nature of the phase boundaries introducing a first order transition.     

Muon spin relaxation measurements in kagomé lattice system SrCr8Ga4O19

Dynamical spin fluctuations in SrCr_8–xGa_4+xO₁₉ a frustrated spin system on a kagomé lattice, is examined by the longitudinal field muon spin relaxation technique. This system shows a spin-glass (SG)-like cusp in the susceptibility atT _g=3.5(2) K. The slowing down of Cr spin fluctuations is found to occur over a very wide temperature rangeT _g<T<30T _g. AsT/T _g 0 these fluctuations remain without static polarization (order parameter). Such strong fluctuations belowT _g have not been observed before in a conventional SG system.     

Model of forming deuteron fluxes and neutron generation in an axial plasma diode with inertial ion confinement

A model of forming deuteron fluxes and neutron generation in an axial plasma diode with two external anodes and a transparent internal hollow cathode is suggested. Such configuration provides longitudinal deuteron oscillations (inertial confinement) and required frequency of collisions with slow deuterons in the cathode plasma. On the basis of the suggested model of neutron generation, the neutron flux generated in the course of D(d, n)³ He nuclear reactions is approximately calculated. The examined diode system seems to be promising for the development of compact controllable neutron sources with increased operation lifetime and transverse size no more than 5 cm.