一簇金刚石晶格上S~4模型的相变

采用重整化群和累积展开的方法,研究了一簇金刚石晶格上S~4模型的相变,求得了系统的临界点.结果表明:当分支数m=2和m 12时,该系统只存在一个Gauss不动点K~*=b_2/2, u_2~*=0;当分支数3≤m≤12时,该系统不仅有Gauss不动点,还存在一个Wilson-Fisher不动点,并且后一个不动点对系统的临界特性产生决定性的影响.     

Critical Behavior of Ising Model with Long Range Correlated Quenched Impurities

The theoretic renormalization-group approach is applied to the study of the critical behavior of the ddimensional Ising model with long-range correlated quenched impurities, which has a power-like correlations r^-(d-p). The asymptotic scaling law is studied in the framework of the expansion in e = 4 - d. In d ~ 4, the dynamic exponent z .is calculated up to the second order in p with ρ= O(ε^1/2). The shape function is obtained in one-loop calculation. When d = 4, the logarithmic corrections to the critical behavior are found. The finite size effect on the order parameter relaxation rate is also studied.     

Critical Behaviors and Finite-Size Scaling of Principal Fluctuation Modes in Complex Systems

Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N×N correlation matrix C can be obtained. The principal fluctuation modes are defined by the eigenvectors of C. Near the critical point of a complex system, we anticipate that the principal fluctuation modes have the critical behaviors similar to that of the susceptibity. With the Ising model on a two-dimensional square lattice as an example, the critical behaviors of principal fluctuation modes have been studied. The eigenvalues of the first 9 principal fluctuation modes have been invesitigated. Our Monte Carlo data demonstrate that these eigenvalues of the system with size L and the reduced temperature t follow a finite-size scaling form λ_n(L, t)=L^γ/ν f_n(tL^1/ν), where γ is critical exponent of susceptibility and ν is the critical exponent of the correlation length. Using eigenvalues λ₁, λ₂ and λ₆, we get the finite-size scaling form of the second moment correlation length ξ(L, t)=Lξ(tL^1/ν). It is shown that the second moment correlation length in the two-dimensional square lattice is anisotropic.     

Coulomb explosion of CS_2 molecule under an intense femtosecond laser field

We experimentally demonstrate the Coulomb explosion process of CS_2 molecule under a near-infrared(800 nm)intense femtosecond laser field by a DC-sliced ion imaging technique. We obtain the DC-sliced images of these fragment ions S~+, S~(2+), CS~+, and CS~(2+)by breaking one C–S bond, and assign their Coulomb explosion channels by considering their kinetic energy release and angular distribution. We also numerically simulate the dissociation dynamics of parent ions CS_2~(k+)(k = 2–4) by a Coulomb potential approximation, and obtain the time evolution of Coulomb energy and kinetic energy release, which indicates that the dissociation time of parent ions CS_2~(k+) decreases with the increase of the charge number k.These experimental and theoretical results can serve as a useful benchmark for those researchers who work in the related area.     

Kawasaki Dynamics on Square Lattice

The bond-moving and decimation renormalization group techniques are applied to obtaining the critical dynamic exponent of the Kawasaki-king model on square lattice. The result is found to be z = z_g + 2, where z_g, is the critical dynamic exponent of the Glauber model on the same lattice. We guess that the relation may be valid for all d-dimensional systems with d≥2.     

Kinetic Gaussian Model with Long-Range Interactions

In this paper dynamical critical phenomena of the Gaussian model with long-range interactions decaying as 1/r^d+δ (δ>0) on d-dimensional hypercubic lattices (d=1, 2, and 3) are studied. First, the critical points are exactly calculated, and it is found that the critical points depend on the value of δ and the range of interactions. Then the critical dynamics is considered. We calculate the time evolutions of the local magnetizations and the spin-spin correlation functions, and further the dynamic critical exponents are obtained. For one-, two- and three-dimensional lattices, it is found that the dynamic critical exponents are all z=2 if δ>2, which agrees with the result when only considering nearest neighboring interactions, and that they are all δ if 0<δ<2. It shows that the dynamic critical exponents are independent of the spatial dimensionality but depend on the value of δ.     

Positivity of energy in five dimensional classical unified field theories, II

Five dimensional classical unified field theories as well as Yang-Mills theory with gauge group U(1), are described in terms of a Lorentzian five dimensional space V₅ with metric tensor γβ which admits a space-like Killing vector ζ. It is assumed that: (1) V₅ has the topology of V₄ x S¹, S¹ is a circle and V₄ is a four dimensional Lorentzian space that is asymptotically flat and (2) the Einstein tensor Γ_β of V₅ satisfies Γ_β Uυ^{β 0} where U and υ are future oriented time-like vectors with γ_βυζ^β = 0. The spinor approach of Witten [4], Nester [3] and Moreschi and Sparling [5] is used to show that the conserved five dimensional energymomentum vector P = ifΓ_β = 0 then V₅ must admit a time-like Killing vector. Lichnerowicz's results [1] then imply that V₅ must be flat. A lower bound for P⁴ (the mass) similar to that found by Gibbons and Hull [6] is obtained.     

Moduli Space of IIB Superstring and SUYM in AdS5 × S5

This paper consists of two parts. In part I, we interpret the hidden symmetry of the moduli space of IIB superstring on AdS₅×S⁵ in terms of the chiral embedding in AdS₅, which turns out to be the CP³ conformal affine Toda model. We review how the position μ of poles in the Riemann-Hilbert formulation of dressing transformation and the value of loop parameter μ in the vertex operator of affine algebra determine the moduli space of the soliton solutions, which describes the moduli space of the Green-Schwarz superstring. We show also how this affine SU(4) symmetry affinizes the conformal symmetry in the twistor space, and how a soliton string corresponds to a Robinson congruence with twist and dilation spin coefficients μ of twistor. In part II, by extending the dressing symmetric action of IIB string in AdS₅×S⁵ to the D₃ brane, we find a gauged WZW action of Higgs Yang-Mills field including the 2-cocycle of axially anomaly. The left and right twistor structures of left and right α-planes glue into an ambitwistor. The symmetry group of Nahm equations is centrally extended to an affine group, thus we explain why the spectral curve is given by affine Toda.     

Critical Behavior of Nonlinear Properties in Percolating Superconductor/Nonlinear-Normal Conductor Networks

The critical behavior of nonlinear response in random networks of superconductor/nonlinear-normal conductors below the percolation threshold is investigated. Two cases are examined: (i) The nonlinear normal conductor has weakly nonlinear current (i)-voltage (ν) response of the form ν = ri + bi^α (bi^α-1《t and α > 1). Both the crossover current density and the crossover electric field are introduced to mark the transition between the linear and nonlinear responses of the network and are found to have power-law dependencies ～(f_c - f)^H and ～(f_c - f)^M as the percolation threshold f_c of the superconductor is approached from below, where H = ν_d - s_d > 0, M = ν_d > 0, ν_d and s_d are the correlation length exponent and the critical exponent of linear conductivity in percolating S/N system respectively; (ii) The nonlinear-normal conductor has strongly nonlinear ν-i response, i.e., i = X^να The effective nonlinear response X_e, behaves as X_e ～(f_c - f)^-W(α), where W ( α ) is the critical exponent of the nonlinear response x_e(α) and is α-dependent in general. The results are compared with recently published data, reasonable agreement is found.     

Preparation of S-TiO2 photocatalyst and photodegradation of L-acid under visible light

S-doped TiO₂ (S-TiO₂) photocatalyst was synthesized by sol–gel method with tetrabutyl titanate and thiourea as precursor. S-TiO₂ was characterized by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), UV–vis absorption spectroscopy, transmission electron microscopy (TEM) and the photocatalytic activity was evaluated by 1-naphthol-5-sulfonic acid (L-acid) under UV, visible light and solar light radiation. The results showed that doped S could improve photoabsorption property of TiO₂ in the visible region, leading the increase in the photocatalytical activity of TiO₂.

The average particle size of the S-TiO₂ photocatalyst is about 10 nm. The S-TiO₂-4 photocatalyst contains 100% anatase crystalline phase of TiO₂. In the S-TiO₂-4 photocatalyst, S does not exist independently, but is incorporated into the crystal lattice of TiO₂. In the inner crystal lattice of the S-TiO₂-4 photocatalyst, S as S²⁻ replaces O in TiO₂, while on the surface of crystal lattice, S exists as S⁴⁺ and S⁶⁺.

The photocatalytical activity of S-TiO₂-4 photocatalyst for the photodegradation of L-acid is better than that of pure TiO₂. Under the same conditions, the photodegradation efficiency of L-acid for the S-TiO₂-4 photocatalyst and the solar light irradiation is 85.1%, while it is only 26.4% for pure TiO₂. In addition, the final products of the photocatalysis of L-acid using the S-TiO₂-4 photocatalyst are not organic compounds with low molecular weight, but the inorganic compounds.     

High—Temperature Cutoff Approximation of the 3D kinetic Ising Model

A single-spin transition critical dynamics is used to investigate the three-dimensional kinetic Ising model on an anisotropic cubic lattice,We first derive the fundamental dynamical equations.and then linearize them by a cutoff approximation.We obtain the approximate solutions of the local magnetization and equal-time pair correlation function approximation.We obtain the approximate solutions of the local magnetization and equal-time pair correlation function in zero field.In which the axial-decoupling terms γ1γ2,γ2γ3and γ1γ3as higher infinitesimal quantity are ignored,where γα=tanh(2k0633)=tanh(2Jα/kβT）（α=1,2,3,)We think that it is reasonable as the temperature of the system is very high.The result of what we obtain in this paper can go back to the one-dimensional Glauber‘s theory as long as k2=k3=0.     

Phase transition and critical behavior of spin–orbital coupled spinel ZnV_2O_4

We present the temperature-dependent susceptibility and specific heat measurement of spinel ZnV_2O_4.The structural transition with orbital ordering and the antiferromagnetic transition with spin ordering were observed at 50 K and 37 K,respectively.By analysis of the hysteresis behavior between the specific heat curves obtained in warming and cooling processes,the structural transition was confirmed to be the first-order transition,while the antiferromagnetic transition was found to be of the second-order type.At the structural transition,the latent heat and entropy change were calculated from the excess specific heat,and the derivative of pressure with respect to temperature was obtained using the Clausius-Clapayron equation.At the magnetic transition,the width of the critical fluctuation region was obtained to be about 0.5 K by comparing with Gaussian fluctuations.In the critical region,the critical behavior was analyzed by using renormalization-group theory.The critical amplitude ratio A~+/A~- = 1.46,which deviates from the 3D Heisenburg model;while the critical exponent α is-0.011,which is close to the 3D XY model.We proposed that these abnormal critical behaviors can be attributed to strong spin-orbital coupling accompanied with the antiferromagnetic transition.Moreover,in the low temperature range(2-5 K),the Fermi energy,the density of states near the Fermi surface,and the low limit of Debye temperature were estimated to be2.42 eV,2.48 eV~(-1),and 240 K,respectively.     

Tricritical and Critical Exponents in Microcanonical Ensemble of Systems with Long-Range Interactions

We explore the tricritical points and the critical lines of both Blume-Emery-Griffiths and Ising model within long-range interactions in the microcanonical ensemble. For K=K_MTP, the tricritical exponents take the values β=1/4, 1=γ^-≠γ⁺=1/2 and 0=α^-≠α⁺=-1/2, which disagree with classical (mean field) values. When K>K_MTP, the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters (K_CTP), where the values of the critical expoents become β=1/2, 1=γ^-≠γ⁺=2 and 0=α⁺≠α⁺=1.     

The Spectra of the Light 0++ Mesons in QCD Sum Rules

In this work, the fight J^PC = 0⁺⁺ mesons f₀(975), a₀(980) and S^*(980) are interpreted as the usual qq states, their masses are investigated in the framework of the QCD sum rules.     

N-cluster correlations in four- and five-dimensional percolation

We study N-cluster correlation functions in four- and five-dimensional (4D and 5D) bond percolation by extensive Monte Carlo simulation. We reformulate the transfer Monte Carlo algorithm for percolation [Phys. Rev. E72, 016126 (2005)] using the disjoint-set data structure, and simulate a cylindrical geometry L^d−1 × ∞, with the linear size up to L = 512 for 4D and 128 for 5D. We determine with a high precision all possible N-cluster exponents, for N =2 and 3, and the universal amplitude for a logarithmic correlation function. From the symmetric correlator with N=2, we obtain the correlationlength critical exponent as 1/ν=1.4610(12) for 4D and 1/ν=1.737(2) for 5D, significantly improving over the existing results. Estimates for the other exponents and the universal logarithmic amplitude have not been reported before to our knowledge. Our work demonstrates the validity of logarithmic conformal field theory and adds to the growing knowledge for high-dimensional percolation.     

A Quantum d-Dimensional Random-Field XY Ferromagnet

We propose a soluble quantum spherical XY ferromagnet with a random field in the boson space. We obtain a general expression of the critical temperat ure T_c below which the ordered ferromagnet phase appears. The Imry-Ma result concerning the lower critical dimension d_c = 4 is recovered, and the critical exponents near the critical temperature T_c are calculated. We show that the random-field fluctuations rather than the quantum fluctuations dominate the phase transition and critical behavior of the system. The entropy vanishes as T^d/2 at low temperatures, contrary to the classical spherical model.     

Magnetic properties of the Bi1.95Sr2.05−xLaxCuOy (Bi-2201) superconducting phase

We have investigated the reversible mixed-state magnetization M of three lanthanum substituted Bi_1.95Sr_2.05−xLa_xCuO_y (Bi-2201) ceramic samples having different critical temperatures T_c ranging from 20.0 to 35.5 K. As for the Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) phase, we found that anisotropy of Bi-2201 is large. A manifestation of this anisotropy is the field independent magnetization M^* observed at a temperature T^*. In the framework of the London model, and including thermal fluctuations of vortices, we found for the temperature dependence of the penetration depth λ_ab(T) = λ_ab(0)[1 − (T/T_c0)ⁿ]^−1/2, with n 1.7 and λ_ab (T = 0) 4000 Å. The estimated upper critical fields μ₀H_c2,c are of the order of 10 T. We observe a peculiar negative slope M/T at low temperature and sufficiently high external magnetic field. This feature seems to be a characteristic of the Bi-2201 phase. However, we do not know whether it is associated with the superconducting mixed-state. A small amount of magnetic impurities could also be responsible for this behavior. Finally, the behavior of the reversible magnetization of the Bi-2201 samples investigated, which are situated at the optimal and in the overdoped region, did not indicate any unusual temperature dependence for the upper critical field H_c2,c.     

Critical behavior in anisotropic cubic systems with long-range interactions

Effects of the potential range of interaction to critical behaviors of anisotropic cubic systems are investigated by means of the Callan-Symanzik equations. As the static critical behavior the stability of fixed points, the critical exponents η^C, γ^C, φ^C_s and φ^C_c, and the equation of state are also investigated. As the dynamic critical behavior the dynamic critical exponent z_φ is derived based on the time-dependent Ginzburg-Landau stochastic model. The two- and three-dimensional critical behaviors are discussed.     

CeFe_(2-x)In_x合金磁性研究与CeFe_(1.95)In_(0.05)合金磁相变临界参数分析

通过等温磁化曲线和等磁场变温曲线测量与标度理论,系统研究了CeFe_(2-x)In_x合金的磁性和CeFe_(1.95)In_(0.05)合金的磁相变临界参数.结果表明:用2.5 at.%的铟替代CeFe_2合金中的铁并不能使合金中的反铁磁态在低温下完全稳定,低场下在2—80 K均能观察到反铁磁相振荡; CeFe_2与CeFe_(1.95)In_(0.05)合金的顺磁-铁磁二级相变居里温度均在230 K附近;在0—5 T磁场范围内, CeFe_(1.95)In_(0.05)合金居里温度处的最大磁熵变为3.13 J/(kg·K),相对制冷量为151.3 J/kg.通过不同方法得到的具有高度自洽性的磁相变标度临界参数均表明CeFe_(1.95)In_(0.05)合金的磁相互作用可以用基于短程相互作用的3D-Ising模型来描述.